https://murray.cds.caltech.edu/api.php?action=feedcontributions&user=Sandberg&feedformat=atomMurray Wiki - User contributions [en]2021-11-29T17:13:00ZUser contributionsMediaWiki 1.35.3https://murray.cds.caltech.edu/index.php?title=Model-Based_Design_and_Qualification_of_Complex_Systems&diff=6032Model-Based Design and Qualification of Complex Systems2007-06-15T21:10:38Z<p>Sandberg: /* Publications */</p>
<hr />
<div>This is a joint project with [http://www.cds.caltech.edu/~doyle John Doyle], funded by Boeing. This page primarily describes the work done in Richard Murray's group.<br />
<br />
{| width=100%<br />
|- valign=top<br />
| width=50% | Current participants:<br />
* {{Julia Braman}}<br />
* Stefano di Cairano (Visiting student, U. Sienna)<br />
* Lijun Chen (CDS postdoc)<br />
* Michael Epstein (PhD student, ME)<br />
* Dennice Gayme (PhD student, CDS)<br />
* Tamas Keviczky (postdoc, CDS)<br />
* Alfred Martinez (PhD student, CDS)<br />
* Demetri Spanos (PhD student, CDS)<br />
* {{Pete Trautman}}<br />
| width=50% | Past participants:<br />
* David Alderson (CDS postdoc, NPS)<br />
* Lijun Chen (CDS PhD)<br />
* Lun Li (PhD student, EE)<br />
* Lars Cremean (ME PhD, Aerovironment)<br />
* Dimitry Kogan (CDS MS)<br />
* Stephen Prajna (CDS PhD)<br />
* Fei Wang (EE PhD; on leave)<br />
| <br />
__TOC__<br />
|}<br />
<br />
== Objectives ==<br />
<br />
The broad goal of this project is to develop new theory, algorithms<br />
and demonstrations of model-based design strategies for complex<br />
systems. This activity is broken up into three broad themes:<br />
* <p>''Robust Yet Fragile Behavior:'' Study the robust-yet-fragile (RYF) nature of complex systems, and specifically to identify the common structures contributing to the RYF behavior, and develop both simple explanatory and detailed predictive models with associated analysis tools.</p><br />
<br />
* <p>''Multi-scale Modeling:'' Systems modeling theory and practice with emphasis on multi-resolution modeling, and managing multiple distinct product representations that must be mapped to each other.</p><br />
<br />
* <p> ''Engineering Implementation:'' Apply analysis and methods in robust-yet-fragile behavior and multi-scale modeling to specific engineering systems of systems that will provide an evaluation of the efficacy of both the framework and the tools toward applications. Two specific testbeds are being used for this purpose: the Caltech multi-vehicle wireless testbed (MVWT) and the Caltech autonomous vehicle testbed ("Alice").</p><br />
<br />
== Publications ==<br />
* D. Alderson, L. Li, W. Willinger, and J. C. Doyle. Understanding Internet topology: Principles, models, and validation. ''IEEE/ACM Transactions on Networking'', 13(6), 2005. <br />
<br />
* D. Alderson and W. Willinger. A contrasting look at self-organization in the Internet and next-generation communication networks. ''IEEE Communications Magazine'', July 2005. <br />
<br />
* J. M. B. Braman, D. A. Wagner and R. M. Murray. [http://www.cds.caltech.edu/~murray/papers/2006m_bwm07-icra.html Fault Tolerance of a Reconfigurable Autonomous Goal-Based Robotic Control System]. 2007 International Confeerence on Robotics and Automation (ICRA), 2007. <br />
<br />
* L. Chen, T. Ho, S. H. Low, and J. C. Doyle. Cross-layer rate control and scheduling in wireless networks with network coding. Technical report, In preparation, 2006. <br />
<br />
* L. Chen, S. H. Low, M. Chiang, and J. C. Doyle. Cross-layer congestion control, routing and scheduling design in ad hoc wireless networks. In ''Proceedings of IEEE Infocom'', 2006. <br />
<br />
* L. Chen, S. H. Low, and J. C. Doyle. Joint congestion control and media access control design for wireless ad hoc networks. In ''Proceedings of IEEE Infocom'', 2005. <br />
<br />
* L. B. Cremean, T. B. Foote, J. H. Gillula, G. H. Hines, D. Kogan, K. L. Kriechbaum, J. C. Lamb, J. Leibs, L. Lindzey, C. E. Rasmussen, A. D. Stewart, J. W. Burdick, and R. M. Murray. {{htdb|2005t_cre+06-jfr|Alice: An information-rich autonomous vehicle for high-speed desert navigation}}. ''Journal of Field Robotics'', 2006. To appear. <br />
<br />
* J.-C. Delvenne, H. Sandberg, and J. C. Doyle. Thermodynamics of Linear Systems. In ''Proceedings of the European Control Conference'', 2007. <br />
<br />
* J. C. Doyle, D. Alderson, L. Li, S. Low, M. Roughan, S. Shalunov, R. Tanaka, and W. Willinger. The ``robust yet fragile'' nature of the Internet. ''Proceedings of the National Academy of Sciences'', 102(41):14497--14502, 2005. <br />
<br />
* D. Gayme, J. C Doyle, S. Prajna, A. Papachristodoulou, and Maryam Fazel. Optimization based methods for determining basins of attraction in the logistic map and set membership in the mandelbrot set. Preprint, 2006. <br />
<br />
* D. Gayme, M. Fazel, and J. C. Doyle. Sos proofs of invariant regions in the logistic map. In ''Proc. IEEE Control and Decision Conference'', 2006. Submitted. <br />
<br />
* S. Glavaski, A. Papachristodoulou, and K. Ariyur. Safety verification of controlled advanced life support system using barrier certificates. In ''Hybrid Systems: Computation and Control'', 2005. <br />
<br />
* D. Kogan. Realtime path planning through optimization methods. Master's thesis, California Institute of Technology, 2005. <br />
<br />
* S. H. Low, J. C. Doyle, L. Li, A. Tang, J. Wang, Optimization Model of Internet Protocols, Proceedings of ACM Sigmetrics, June 2005.<br />
<br />
* S. Prajna and A. Jadbabaie. Safety verification of hybrid systems using barrier certificates. In ''Hybrid Systems: Computation and Control'', 2004. <br />
<br />
* S. Prajna and A. Jadbabaie. Methods for safety verification of time-delay systems. In ''Proceedings of the IEEE Conference on Decision and Control'', 2005. <br />
<br />
* S. Prajna, A. Jadbabaie, and G. J. Pappas. Stochastic safety verification using barrier certificates. In ''Proceedings of the IEEE Conference on Decision and Control'', 2004. <br />
<br />
* S. Prajna, A. Papachristodoulou, P. J. Seiler, and P. A. Parrilo. SOSTOOLS -- Sum of Squares Optimization Toolbox, User's Guide. Available at http://www.cds.caltech.edu/sostools and http://www.mit.edu/~parrilo/sostools, 2002, 2004. <br />
<br />
* S. Prajna and A. Rantzer. On the necessity of barrier certificates. In ''Proceedings of the IFAC World Congress'', 2005. <br />
<br />
* S. Prajna and A. Rantzer. Primal-dual tests for safety and reachability. In ''Hybrid Systems: Computation and Control''. Springer-Verlag, 2005. <br />
<br />
* H. Sandberg, J.-C. Delvenne, and J. C. Doyle. The Statistical Mechanics of Fluctuation-Dissipation and Measurement Back Action. In ''Proceedings of the American Control Conference'', 2007.<br />
<br />
* H. Sandberg, J.-C. Delvenne, and J. C. Doyle. Linear-Quadratic-Gaussian Heat Engines. Submitted, 2007.<br />
<br />
* H. Sandberg and R. M. Murray. Frequency-Weighted Model Reduction with Applications to Structured Models. In ''Proceedings of the American Control Conference'', 2007.<br />
<br />
* J. Wang, L. Li, S. H. Low, and J. C. Doyle. Cross-layer optimization in tcp/ip networks. ''IEEE/ACM Transactions on Networking'', 13(3), 2006.<br />
<br />
== Reports ==<br />
* [[Media:boeing_report-mar06.pdf|Annual report, January 2005 to March 2006]]<br />
<br />
== Software ==<br />
* SOSTOOLS<br />
<br />
== Related Activities ==<br />
* [[Connections II]] - Workshop on Foundations of Network Science (Caltech, August 2006)<br />
* [http://www.cds.caltech.edu/~murray/VaVmuri V&V MURI] - Specification, Design and Verification of Distributed Embedded Systems (AFOSR MURI)</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Group_Schedule,_Summer_2007&diff=6013Group Schedule, Summer 20072007-06-04T16:27:22Z<p>Sandberg: /* Group Meetings */</p>
<hr />
<div>This page contains information about various upcoming events that are of interest to the group. __NOTOC__<br />
{| width=100%<br />
|- valign=top<br />
| width=50% |<br />
* [[June 2007 Meetings]]<br />
* [[Summer 2007 Meeting Schedule]]<br />
| width=50% |<br />
* [[Group Schedule, Spring 2007]]<br />
|}<br />
<br />
== Group Meetings ==<br />
Group meetings are on Tuesdays at 6 pm in 114 Steele. Visitors are welcome (but be prepared to get signed up to give a talk!).<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=30% |<br />
{{agenda begin}}<br />
{{agenda item|Date|Speaker}}<br />
{{agenda item|12 Jun|No group meeting (DGC)}}<br />
{{agenda item|19 Jun|Open}}<br />
{{agenda item|26 June|John}}<br />
{{agenda item|3 Jul|Henrik}}<br />
{{agenda item|10 Jul|No group meeting (ACC)}}<br />
{{agenda end}}<br />
| width=30% |<br />
{{agenda begin}}<br />
{{agenda item|Date|Speaker}}<br />
{{agenda item|17 Jul|Ling}}<br />
{{agenda item|24 Jul|Tim}}<br />
{{agenda item|31 Jul|Mary}}<br />
{{agenda item|7 Aug|No group meeting (AFOSR)}}<br />
{{agenda item|14 Aug|Waydo}}<br />
{{agenda end}}<br />
| width=30% |<br />
{{agenda begin}}<br />
{{agenda item|Date|Speaker}}<br />
{{agenda item|21 Aug|Nok}}<br />
{{agenda item|28 Aug|No group meeting (travel)}}<br />
{{agenda item|4 Sep|Julia}}<br />
{{agenda item|11 Sep|Dom}}<br />
{{agenda item|18 Sep|Michael}}<br />
{{agenda end}}<br />
|}</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Summer_2007_Meeting_Schedule&diff=5999Summer 2007 Meeting Schedule2007-06-03T16:56:24Z<p>Sandberg: /* Wed */</p>
<hr />
<div>__NOTOC__<br />
Meetings will start on '''18 June'''.<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=25% |<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item|3:00p| Open}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Open}}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item|3:00p| Stefano}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Open}}<br />
{{agenda item|6:00p|[[Group Schedule|Group Meeting]]}}<br />
{{agenda item|7:00p| Zhipu/Ling <br>(alt weeks) }}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item||}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Henrik}}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Julia}}<br />
{{agenda item|3:00p| Open}}<br />
{{agenda item|4:00p| Waydo}}<br />
{{agenda item|5:00p| Nok}}<br />
{{agenda end}}<br />
|<br />
<br />
|}</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Summer_2007_Meeting_Schedule&diff=5998Summer 2007 Meeting Schedule2007-06-03T16:55:48Z<p>Sandberg: /* Mon */</p>
<hr />
<div>__NOTOC__<br />
Meetings will start on '''18 June'''.<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=25% |<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item|3:00p| Open}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Open}}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item|3:00p| Stefano}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Open}}<br />
{{agenda item|6:00p|[[Group Schedule|Group Meeting]]}}<br />
{{agenda item|7:00p| Zhipu/Ling <br>(alt weeks) }}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item||}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Open}}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Julia}}<br />
{{agenda item|3:00p| Open}}<br />
{{agenda item|4:00p| Waydo}}<br />
{{agenda item|5:00p| Nok}}<br />
{{agenda end}}<br />
|<br />
<br />
|}</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Summer_2007_Meeting_Schedule&diff=5997Summer 2007 Meeting Schedule2007-06-03T16:53:59Z<p>Sandberg: /* Mon */</p>
<hr />
<div>__NOTOC__<br />
Meetings will start on '''18 June'''.<br />
{| width=100% border=1<br />
|- valign=top<br />
| width=25% |<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item|3:00p| Open}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Henrik}}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item|3:00p| Stefano}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Open}}<br />
{{agenda item|6:00p|[[Group Schedule|Group Meeting]]}}<br />
{{agenda item|7:00p| Zhipu/Ling <br>(alt weeks) }}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Open}}<br />
{{agenda item||}}<br />
{{agenda item|4:00p| Open}}<br />
{{agenda item|5:00p| Open}}<br />
{{agenda end}}<br />
| width=25% |<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p| Julia}}<br />
{{agenda item|3:00p| Open}}<br />
{{agenda item|4:00p| Waydo}}<br />
{{agenda item|5:00p| Nok}}<br />
{{agenda end}}<br />
|<br />
<br />
|}</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=June_2007_Meetings&diff=5996June 2007 Meetings2007-06-03T16:52:48Z<p>Sandberg: /* Wed, 13 Jun */</p>
<hr />
<div>The list below has times that I am available to meet between 4 June and 15 June. Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and see if you can switch). __NOTOC__<br />
<br />
<br><br />
<table width=100% border=1><br />
<tr valign=top><td width=20%><br />
==== Mon, 4 Jun ====<br />
Travel<br />
</td><td width=20%><br />
==== Tue, 5 Jun ====<br />
{{agenda begin}}<br />
{{agenda item|4:00p|Tamas}}<br />
{{agenda item|4:30p|Open}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Wed, 6 June ====<br />
{{agenda begin}}<br />
{{agenda item|5:00p|Tim}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Thu, 7 Jun ====<br />
{{agenda begin}}<br />
{{agenda item|3:00p|Elisa}}<br />
{{agenda item|4:00p|Waydo}}<br />
{{agenda item|5:00p|Julia}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Fri, 8 Jun ====<br />
Commencement<br />
</td></tr><br />
</table><br />
<br />
<br><br />
<table width=100% border=1><br />
<tr valign=top><td width=20%><br />
<br />
==== Mon, 11 Jun ====<br />
DARPA preparations<br />
<br />
</td><td width=20%><br />
<br />
==== Tue, 12 Jun ====<br />
DARPA Site Visit<br />
* Morning: demos at Santa Anita, north lot<br />
* Afternoon: DARPA site visit<br />
<br />
No group meeting<br />
</td><td width=20%><br />
<br />
==== Wed, 13 Jun ====<br />
{{agenda begin}}<br />
{{agenda item|9:00a|DGC SURF <br> + Nok, Sam, Noel}}<br />
{{agenda item|10:00a|Synbio SURF <br>+ Mary, Elisa}}<br />
{{agenda item||}}<br />
{{agenda item|4:00p|Henrik}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Thu, 14 Jun ====<br />
{{agenda begin}}<br />
{{agenda item|2:00p|Open}}<br />
{{agenda item|3:00p|Stefano}}<br />
{{agenda item|4:00p|Open}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Fri, 15 Jun ====<br />
Travel<br />
</td></tr><br />
</table></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=April_2007_Meetings&diff=5927April 2007 Meetings2007-04-18T03:25:39Z<p>Sandberg: /* Mon, 30 Apr */</p>
<hr />
<div>The list below has times that I am available to meet between 15 and 22 April. Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and figure out how much of a bribe is required to get them to switch). __NOTOC__<br />
<br />
<br><br />
<table width=100% border=1><br />
<tr valign=top><td width=20%><br />
==== Sun, 15 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Mon, 16 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|10:30a|Pete}}<br />
{{agenda item|11:30a|Henrik (30m)}}<br />
{{agenda item|6:30p|Tim}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Tue, 17 April ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a|Melvin}}<br />
{{agenda item|11:00a|Stefano}}<br />
{{agenda item|2:00p|Ling}}<br />
{{agenda item|7:00p|Mike}}<br />
{{agenda item|8:00p|Open (45m)}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Wed-Fri ====<br />
Princeton<br />
</td><td width=20%><br />
<br />
==== Sun, 22 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|3:00p|Danielle}}<br />
{{agenda item|4:00p|Nok}}<br />
{{agenda item|5:00p|Zhipu}}<br />
{{agenda item|6:00p|Maryam?}}<br />
{{agenda end}}<br />
</td></tr><br />
</table><br />
<br />
<br><br />
<table width=100% border=1><br />
<tr valign=top><td width=20%><br />
<br />
==== Mon, 23 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|10:30a|John}}<br />
{{agenda item|11:00a|Julia (30 min)}}<br />
{{agenda item|1:30p|Mary}}<br />
{{agenda item|2:30p|Elisa}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Tue-Thu ====<br />
Cornell<br />
</td><td width=20%><br />
<br />
==== Fri, 27 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Sun, 29 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|4:00p|Open}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Mon, 30 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|10:30a|Julia}}<br />
{{agenda item|11:30a|Henrik}}<br />
{{agenda item|1:00p|Open}}<br />
{{agenda item|2:00p|Ling}}<br />
{{agenda item|3:00p|Mary, Elisa}}<br />
{{agenda item|6:30p|Open}}<br />
{{agenda end}}<br />
</td></tr><br />
</table><br />
--></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=April_2007_Meetings&diff=5913April 2007 Meetings2007-04-15T01:48:32Z<p>Sandberg: /* Mon, 16 Apr */</p>
<hr />
<div>The list below has times that I am available to meet between 15 and 22 April. Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and figure out how much of a bribe is required to get them to switch). __NOTOC__<br />
<br />
<br><br />
<table width=100% border=1><br />
<tr valign=top><td width=20%><br />
==== Sun, 15 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Mon, 16 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|10:30a|Open}}<br />
{{agenda item|11:00a|Henrik (30m)}}<br />
{{agenda item|6:30p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Tue, 17 April ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a|Melvin}}<br />
{{agenda item|11:00a|Stefano}}<br />
{{agenda item|2:00p|Ling}}<br />
{{agenda item|7:00p|Open}}<br />
{{agenda item|8:00p|Open (45m)}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Wed-Fri ====<br />
Princeton<br />
</td><td width=20%><br />
<br />
==== Sun, 22 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|3:00p|Open}}<br />
{{agenda item|4:00p|Nok}}<br />
{{agenda item|5:00p|Zhipu}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td></tr><br />
</table><br />
<br />
<br><br />
<!--<br />
<table width=100% border=1><br />
<tr valign=top><td width=20%><br />
<br />
==== Mon, 23 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|10:30a|John}}<br />
{{agenda item|11:00a|Open (30 min)}}<br />
{{agenda item|1:30p|Open}}<br />
{{agenda item|2:30p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Tue-Thu ====<br />
Cornell<br />
</td><td width=20%><br />
<br />
==== Fri, 27 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|3:30p|Hold for now}}<br />
{{agenda item|4:30p|Hold for now}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Sun, 29 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|4:00p|Open}}<br />
{{agenda item|5:00p|Open}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td><td width=20%><br />
<br />
==== Mon, 30 Apr ====<br />
{{agenda begin}}<br />
{{agenda item|10:30a|Open}}<br />
{{agenda item|11:30a|Open}}<br />
{{agenda item|1:00p|Hold for now}}<br />
{{agenda item|2:00p|Hold for now}}<br />
{{agenda item|3:00p|Mary, Elisa}}<br />
{{agenda item|6:30p|Open}}<br />
{{agenda end}}<br />
</td></tr><br />
</table><br />
--></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=March_2007_Meetings&diff=5849March 2007 Meetings2007-03-03T21:11:21Z<p>Sandberg: /* Wednesday, 14 Mar */</p>
<hr />
<div>The list below has times that I am available to meet between 5 and 16 March. Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and figure out how much of a bribe is required to get them to switch). Please only sign up for one time slot; if we need to meet a second time we can arrange that separately. __NOTOC__<br />
<br />
<table width=100% border=1><br />
<tr valign=top><td><br />
==== Monday, 5 March ====<br />
{{agenda begin}}<br />
{{agenda item|3:00p|Open}}<br />
{{agenda item|4:00p|Ling}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Tuesday, 6 March ====<br />
{{agenda begin}}<br />
{{agenda item|3:00p|Tim}}<br />
{{agenda item|4:00p|stefano}}<br />
{{agenda item|5:00p|Zhipu}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Wednesday, 7 March ====<br />
{{agenda begin}}<br />
{{agenda item|12:00p|Julia}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Sunday, 11 Mar ====<br />
{{agenda begin}}<br />
{{agenda item|4:00p|Open}}<br />
{{agenda item|5:00p|Nok}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda end}}<br />
</td></tr><br />
</table><br />
<br />
<br><br />
<br />
<table width=100% border=1><br />
<tr valign=top><td><br />
<br />
==== Monday, 12 Mar ====<br />
{{agenda begin}}<br />
{{agenda item|9:30a|Mary}}<br />
{{agenda item|10:30a|Dom}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Wednesday, 14 Mar ====<br />
{{agenda begin}}<br />
{{agenda item|3:30p|Henrik}}<br />
{{agenda item|4:30p|Open}}<br />
{{agenda item|5:30p|Melvin}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Thursday, 15 Mar ====<br />
{{agenda begin}}<br />
{{agenda item|6:00p|Open}}<br />
{{agenda item|7:00p|Open}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Friday, 16 Mar ====<br />
{{agenda begin}}<br />
{{agenda item|6:00p|Fei}}<br />
{{agenda end}}<br />
</td></tr></table></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Winter_2007_Meeting_Schedule&diff=5389Winter 2007 Meeting Schedule2007-01-01T23:09:21Z<p>Sandberg: /* Mon */</p>
<hr />
<div>__NOTOC__<br />
{| width=100% border=1<br />
|- valign=top<br />
|<br />
==== Mon ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a| Open }}<br />
{{agenda item|11:00a| Henrik }}<br />
{{agenda end}}<br />
|<br />
<br />
==== Tue ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a| Open }}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|2:00p| Open }}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|6:00p|[[Group Schedule|Group Meeting]]}}<br />
{{agenda item|7:00p| Open }}<br />
{{agenda end}}<br />
|<br />
==== Wed ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a| Julia }}<br />
{{agenda item|11:00a| Open }}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p| Ling }}<br />
{{agenda item|6:00p| Open }}<br />
{{agenda end}}<br />
|<br />
<br />
==== Thu ====<br />
{{agenda begin}}<br />
{{agenda item|10:00a| Open }}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|2:00p| Open }}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|5:00p| Open }}<br />
{{agenda item|6:00p| Open }}<br />
{{agenda end}}<br />
|<br />
==== Fri ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|11:00a| Open }}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|3:00p| Open }}<br />
{{agenda item|4:00p| Open }}<br />
{{agenda end}}<br />
|}</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Fall_2006_Meeting_Schedule&diff=4630Fall 2006 Meeting Schedule2006-09-17T17:28:01Z<p>Sandberg: /* Monday */</p>
<hr />
<div><table width=100% border=1><br />
<tr valign=top><td><br />
==== Monday ====<br />
{{agenda begin}}<br />
{{agenda item||}}<br />
{{agenda item|9:45-10:30|Ling}}<br />
{{agenda item|10:30-11:15|Open}}<br />
{{agenda item|11:15-12:00|Henrik}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item||}}<br />
{{agenda item|5:00-5:45|Nok}}<br />
{{agenda item|5:45-6:30|Open}}<br />
{{agenda item|6:30-7:15|Open}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Tuesday ====<br />
{{agenda begin}}<br />
{{agenda item|9:00-9:45|Mary}}<br />
{{agenda item|9:45-10:30|John}}<br />
{{agenda item|10:30-11:15|Mike}}<br />
{{agenda item|11:15-12:00|Waydo}}<br />
{{agenda item||}}<br />
{{agenda item|2:15-3:00|Tim}}<br />
{{agenda item||}}<br />
{{agenda item|5:15-6:00|Zhipu}}<br />
{{agenda item|6:00-7:00|[[Group Schedule|Group Meeting]]}}<br />
{{agenda item|7:15-8:00|Open}}<br />
{{agenda item|8:00-8:45|Open}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Wednesday ====<br />
{{agenda begin}}<br />
{{agenda item|9:00-9:45|Melvin}}<br />
{{agenda item|9:45-10:30|Julia}}<br />
{{agenda item|10:30-11:15|Stefano}}<br />
{{agenda item|11:15-12:00|Elisa}}<br />
{{agenda end}}<br />
</td></tr></table></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=August_2006_meeting_schedule&diff=4370August 2006 meeting schedule2006-08-12T20:30:32Z<p>Sandberg: /* Monday, 28 Aug */</p>
<hr />
<div>The list below has times that I am available to meet between 21 August and 1 September. Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and figure out how much of a bribe is required to get them to switch). Please only sign up for one time slot; if we need to meet a second time we can arrange that separately. __NOTOC__<br />
<br />
<table width=100% border=1><br />
<tr valign=top><td><br />
==== Monday, 21 Aug ====<br />
{{agenda begin}}<br />
{{agenda item|4:00-4:45|Elisa Franco}}<br />
{{agenda item|4:45-5:30|Open}}<br />
{{agenda item|5:30-6:15|Open}}<br />
{{agenda item|6:15-7:00|Open}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Thursday, 24 Aug ====<br />
{{agenda begin}}<br />
{{agenda item|2:00-2:45|Open}}<br />
{{agenda item|2:45-3:30|Open}}<br />
{{agenda item|3:30-4:15|Open}}<br />
{{agenda item|4:15-5:00|Open}}<br />
{{agenda item|5:00-5:45|Open}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Friday, 25 Aug ====<br />
{{agenda begin}}<br />
{{agenda item|2:00-2:45|Open}}<br />
{{agenda item|2:45-3:30|Open}}<br />
{{agenda item|3:30-4:15|Open}}<br />
{{agenda item|4:15-5:00|Open}}<br />
{{agenda item|5:00-5:45|Open}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Monday, 28 Aug ====<br />
{{agenda begin}}<br />
{{agenda item|2:00-2:45|Henrik Sandberg}}<br />
{{agenda item|2:45-3:30|Open}}<br />
{{agenda item|3:30-4:15|John Carson}}<br />
{{agenda item|4:15-5:00|Fei Wang}}<br />
{{agenda item|5:00-5:45|Open}}<br />
{{agenda end}}<br />
</td></tr></table></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=July_2006_meeting_schedule&diff=4196July 2006 meeting schedule2006-06-27T21:43:49Z<p>Sandberg: /* Tuesday, 11 July */</p>
<hr />
<div>The list below has times that I am available to meet between 5 July and 12 July. Please pick a time that works and fill in your name. If none of the times work, send me e-mail (or find someone else who has a slot that does work and figure out how much of a bribe is required to get them to switch). Please only sign up for one time slot; if we need to meet a second time we can arrange that separately. __NOTOC__<br />
<br />
<table width=100% border=1><br />
<tr valign=top><td><br />
==== Wednesday, 5 July ====<br />
{{agenda begin}}<br />
{{agenda item|10:30-11:15|Open}}<br />
{{agenda item|11:15-12:00|Ling Shi}}<br />
{{agenda item||}}<br />
{{agenda item|3:30-4:15|Open}}<br />
{{agenda item|4:15-5:00|Open}}<br />
{{agenda item|5:00-5:45|Nok}}<br />
{{agenda item|5:45-6:30|Vijay Gupta}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Thursday, 6 July ====<br />
{{agenda begin}}<br />
{{agenda item|9:45-10:30|Open}}<br />
{{agenda item|10:30-11:15|Michael Epstein}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Friday, 7 July ====<br />
{{agenda begin}}<br />
{{agenda item|10:30-11:15|Open}}<br />
{{agenda item|11:15-12:00|Ketan Savla}}<br />
{{agenda item||}}<br />
{{agenda item|3:00-3:45|Open}}<br />
{{agenda item|3:45-4:30|Open}}<br />
{{agenda item|4:30-5:15|Open}}<br />
{{agenda item|5:15-6:00|Open}}<br />
{{agenda end}}<br />
</td><td><br />
<br />
==== Tuesday, 11 July ====<br />
{{agenda begin}}<br />
{{agenda item|9:45-10:30|Mary Dunlop}}<br />
{{agenda item|10:30-11:15|Henrik Sandberg}}<br />
{{agenda item|11:15-12:00|Open}}<br />
{{agenda end}}<br />
</td></tr></table></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3755NCS: Moving Horizon Estimation2006-05-01T04:52:01Z<p>Sandberg: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L4-2_MHE.pdf|Lecture: Moving Horizon Estimation]]<br />
* [[Media:Stateestim.pdf|Lecture notes: State estimation]]<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.</p><br />
<br />
* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives an introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --><br />
* <p>[http://jbrwww.che.wisc.edu/theses/rao.ps Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems] C.V. Rao. Rao's PhD thesis contains a lot of material on MHE. There is also a discussion on MAP estimates.</p><br />
* <p>[http://www.eng.newcastle.edu.au/eecs/cdsc/books/cce/ Constrained Control and Estimation - An Optimisation Approach], G. C. Goodwin, M. M. Seron, J. A. De Dona. Springer Verlag, 2005. This is a recent book treating constrained control and estimation in a unified framework (including finite horizon optimal control and RHC) using discrete-time formulation. The website has a lot of additional useful and interesting material.</p></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3754NCS: Kalman Filtering2006-05-01T04:51:17Z<p>Sandberg: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. How the filter deals with sensor fusion is discussed and an example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
* [[Media:L4-1_Kalman.pdf|Lecture: Kalman Filtering]]<br />
* [[Media:Stateestim.pdf|Lecture notes: State estimation]]<br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=File:Stateestim.pdf&diff=3753File:Stateestim.pdf2006-05-01T04:47:22Z<p>Sandberg: Preliminary lecture notes on state estimation.</p>
<hr />
<div>Preliminary lecture notes on state estimation.</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3620NCS: Moving Horizon Estimation2006-04-20T00:36:32Z<p>Sandberg: /* Additional Resources */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
[[Media:L4-2_MHE.pdf|Lecture: Moving Horizon Estimation]]<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.</p><br />
<br />
* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives an introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --><br />
* <p>[http://jbrwww.che.wisc.edu/theses/rao.ps Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems] C.V. Rao. Rao's PhD thesis contains a lot of material on MHE. There is also a discussion on MAP estimates.</p><br />
* <p>[http://www.eng.newcastle.edu.au/eecs/cdsc/books/cce/ Constrained Control and Estimation - An Optimisation Approach], G. C. Goodwin, M. M. Seron, J. A. De Dona. Springer Verlag, 2005. This is a recent book treating constrained control and estimation in a unified framework (including finite horizon optimal control and RHC) using discrete-time formulation. The website has a lot of additional useful and interesting material.</p></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3619NCS: Moving Horizon Estimation2006-04-20T00:35:23Z<p>Sandberg: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
[[Media:L4-2_MHE.pdf|Lecture: Moving Horizon Estimation]]<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.</p><br />
<br />
* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives an introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --><br />
* <p>[http://jbrwww.che.wisc.edu/theses/rao.ps Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems] C.V. Rao. Rao's PhD thesis contains a lot of material on MHE. There is also a discussion on MAP estimates.</p></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=File:L4-2_MHE.pdf&diff=3618File:L4-2 MHE.pdf2006-04-20T00:33:59Z<p>Sandberg: Slides for the moving horizon estimation lecture.</p>
<hr />
<div>Slides for the moving horizon estimation lecture.</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3617NCS: Moving Horizon Estimation2006-04-19T18:22:44Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.</p><br />
<br />
* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives an introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --><br />
* <p>[http://jbrwww.che.wisc.edu/theses/rao.ps Moving Horizon Strategies for the Constrained Monitoring and Control of Nonlinear Discrete-Time Systems] C.V. Rao. Rao's PhD thesis contains a lot of material on MHE. There is also a discussion on MAP estimates.</p></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3616NCS: Moving Horizon Estimation2006-04-19T17:17:40Z<p>Sandberg: /* Reading */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.</p><br />
<br />
* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives an introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3615NCS: Moving Horizon Estimation2006-04-19T17:16:13Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.</p><br />
<br />
* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives a brief introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3614NCS: Moving Horizon Estimation2006-04-19T17:15:32Z<p>Sandberg: /* Reading */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences between the methods and when EKF is likely to fail.<br />
<br />
* <p>[http://ieeexplore.ieee.org/xpls/abs_all.jsp?isnumber=26479&arnumber=1178905&count=27&index=5 Constrained State Estimation for Nonlinear Discrete-Time Systems: Stability and Moving Horizon Approximations], C.V. Rao, J.B. Rawlings, and D.Q. Mayne, ''IEEE Transactions on Automatic Control'', vol.48, no.2, 2003. A mathematical treatment of MHE and stability conditions are derived. Everybody should read at least Section I.<br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives a brief introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3613NCS: Moving Horizon Estimation2006-04-19T17:09:04Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receding horizon control (RHC) and also relies on optimization software. The lecture ends with a brief discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
* <p>[http://pubs.acs.org/cgi-bin/abstract.cgi/iecred/2005/44/i08/abs/ie034308l.html Critical evaluation of extended Kalman filtering and moving horizon estimation], E.L. Haseltine and J.B. Rawlings, ''Ind. Eng. Chem. Res.'', vol. 44, no.8, 2005. Contains several examples where EKF and MHE have been applied. Discusses the differences.<br />
<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. Gives a brief introduction to the extended Kalman filter in discrete time.</p><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3612NCS: Moving Horizon Estimation2006-04-19T16:59:24Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space, as well as asymmetric probability distributions, into account. MHE is dual to receeding horizon control (RHC) and also relies on optimization software. The lecture ends with a bried discussion on stability properties of MHE.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3611NCS: Moving Horizon Estimation2006-04-19T16:51:58Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up<br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture. --><br />
<br />
In this lecture, we give an introduction to moving horizon estimation (MHE) and extended Kalman filters (EKF). These filter stuctures can be used with nonlinear models and are therefore more general than the standard Kalman filter. Furthermore, MHE can also take constraints on the noise and the state space into account, and deal with asymmetric probability distributions.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Moving_Horizon_Estimation&diff=3610NCS: Moving Horizon Estimation2006-04-19T16:34:23Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3588NCS: Kalman Filtering2006-04-18T01:03:58Z<p>Sandberg: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. How the filter deals with sensor fusion is discussed and an example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
[[Media:L4-1_Kalman.pdf|Lecture: Kalman Filtering]]<br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=File:L4-1_Kalman.pdf&diff=3587File:L4-1 Kalman.pdf2006-04-18T01:02:27Z<p>Sandberg: Slides on Kalman filtering for CDS 270-2.</p>
<hr />
<div>Slides on Kalman filtering for CDS 270-2.</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3586NCS: Kalman Filtering2006-04-17T23:13:42Z<p>Sandberg: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. How the filter deals with sensor fusion is discussed and an example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
[http://www.cds.caltech.edu/~henriks/L4-4_Kalman.pdf Kalman Filtering]<br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3585NCS: Kalman Filtering2006-04-17T23:13:06Z<p>Sandberg: /* Lecture Materials */</p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. How the filter deals with sensor fusion is discussed and an example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
[[http://www.cds.caltech.edu/~henriks/L4-4_Kalman.pdf Kalman Filtering]]<br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3560NCS: Kalman Filtering2006-04-16T00:22:34Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. How the filter deals with sensor fusion is discussed and an example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3559NCS: Kalman Filtering2006-04-16T00:19:17Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of filtering problems and the Kalman filter. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3558NCS: Kalman Filtering2006-04-16T00:18:19Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop. A brief introduction to the Kalman filter in discrete time. No proofs are given, but it is a good first read.</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter] A webpage that gives a proof and some applications.</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. A classical paper. Still very readable. It uses different notation than the lecture, and present a different and more general proof. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop. A webpage with many links on Kalman filter.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005. A reissue of a book from 1979. It contains a detailed mathematical presentation of the filtering problems. A very good book.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3557NCS: Kalman Filtering2006-04-16T00:10:56Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter]</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/ The Kalman Filter], G. Welch and G. Bishop.</p><br />
<br />
* <p>[http://www.amazon.com/gp/product/0486439380/102-3301256-1504117?v=glance&n=283155 Optimal Filtering], B.D.O Anderson and J.B. Moore. Dover Books on Engineering, 2005.</p><br />
<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3556NCS: Kalman Filtering2006-04-16T00:06:11Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf An Introduction to the Kalman Filter], G. Welch and G. Bishop</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter]</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3555NCS: Kalman Filtering2006-04-16T00:05:30Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html An Introduction to the Kalman Filter], G. Welch and G. Bishop</p><br />
<br />
* <p>[http://en.wikipedia.org/wiki/Kalman_filter Wikipedia: Kalman Filter]</p><br />
<br />
* <p>[http://www.cs.unc.edu/~welch/kalman/kalmanPaper.html A New Approach to Linear Filtering and Prediction Problem], R.E. Kalman. ''Transactions of the ASME'', Series D, 1960. </p><br />
<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3554NCS: Kalman Filtering2006-04-15T23:40:48Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we study the Kalman filter for discrete-time linear systems. In particular, we see under what assumptions and in what senses the Kalman filter is an optimal estimator. To prove the results we use some results about conditional expectations and Gaussian probabiliy distributions. We show that the filter contains one prediction step and one correcter step that takes the most recent measurement into account. An example is used to illustrate the results.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading <br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3486NCS: Kalman Filtering2006-04-11T02:59:11Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
In this lecture, we will study and derive the Kalman filter. In particular, we will see under what assumptions and in what sense the Kalman filter is optimal.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=NCS:_Kalman_Filtering&diff=3485NCS: Kalman Filtering2006-04-11T02:53:04Z<p>Sandberg: </p>
<hr />
<div>{{cds270-2 header}} <!-- Generates the header, including table of contents and link back to main page --><br />
<br />
<!-- Enter a 1 paragraph description of the contents of the lecture. Make sure to include any key concepts, so that the wiki search feature will pick them up --><br />
This is the template for CDS 270 lectures. If you edit this page, you will see comments describing what goes in each section. '''Do not edit this template.''' See [[CDS 270: Information for Lecturers]] for more information on how to create a wiki page corresponding to a lecture.<br />
<br />
== Lecture Materials ==<br />
<!-- Include links to materials that you used in your lecture. At a minimum, this should include a link to your lecture presentation. You might also include links to MATLAB scripts or other source code that students would find useful --><br />
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] --><br />
<br />
== Reading ==<br />
<!-- A reading list for the lecture. This will typically be 3-5 articles or book chapters that are particularly relevant to the material being presented. The reading list should be annotated to explain how the articles fit into the topic for the lecture. --><br />
<br />
== Additional Resources ==<br />
<!-- Links to additional information. If there are good sources of additional information for students interested in exploring this topic further, these should go at the bottom of the page. --></div>Sandberghttps://murray.cds.caltech.edu/index.php?title=CDS_270-2,_Spring_2006&diff=3484CDS 270-2, Spring 20062006-04-11T02:51:56Z<p>Sandberg: /* Course Schedule */</p>
<hr />
<div><table width="100%" cellspacing=0><br />
<tr valign=top><br />
<td rowspan=2 align=center> [[Image:citlogo.png|75px]]<br />
<td align=center><font color='blue' size='+2'>Networked Control Systems</font><br />
<td rowspan=2 align=center> [[Image:cdslogo.png|90px]]<br />
<tr valign=top><td align=center><font color='blue' size='+1'>Spring 2006</font><br />
</table><br />
<br />
<table align=right><tr><td>__TOC__</table><br />
<table cellspacing=0 cellpadding=0><br />
<tr valign=top><br />
<td width=60%><br />
* Instructor: [[User:Murray|Richard M. Murray]]<br />
* Co-instructors: [[User:Keviczky|Tamas Keviczky]], [[User:Mostofi|Yasi Mostofi]], [[User:Sandberg|Henrik Sandberg]], [[User:Sinopoli|Bruno Sinopoli]]<br />
<td align=center><br />
<table cellpadding=0 cellspacing=0><tr><td><br />
* [[Media:cds270-2_syllabus_sp06.pdf|Course syllabus]]<br />
* [http://listserv.cds.caltech.edu/mailman/listinfo/cds270 Course mailing list]<br />
* [[CDS 270: Information for Lecturers|Information for lecturers]]<br />
</table><br />
<tr><td colspan=2><br />
* Graduate instructors: Vijay Gupta, Zhipu Jin, Ling Shi, Demetri Spanos<br />
* Lectures: MWF 2-3 pm, 125 Steele<br />
</table><br />
<br />
== Course Schedule ==<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading<br />
|-<br />
| align=center rowspan=5 | 1 <br />
| colspan=3 | '''Introduction to Networked Control Systems (R. Murray)'''<br />
|-<br />
| 27 Mar (M)<br />
| [[NCS: Introduction|Course overview, applications and administration]]<br />
| [[Media:cds270-2_syllabus_sp06.pdf|Syllabus]]; {{ncsbook|introduction|Ch 1}}<br />
|-<br />
| 29 Mar (W)<br />
| [[Alice: Introduction|Case study: Alice]]<br />
| [http://www.cds.caltech.edu/~murray/papers/2005t_cre+06-jfr.html Cremean et al, 2005]<br />
|-<br />
| colspan=3 | '''Networked embedded systems programming (R. Murray)'''<br />
|-<br />
| 31 Mar (F)<br />
| [[NCS: Message Transfer Systems|Message transfer systems: spread]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://portal.acm.org/citation.cfm?id=359563 Lamport, 1978]<br />
|-<br />
| align=center rowspan=3 | 2<br />
| 3 Apr (M)<br />
| [[NCS: Multi-Threaded Control Systems|Multi-threaded control systems: pthreads]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://www.llnl.gov/computing/tutorials/pthreads Pthreads]<br />
|-<br />
| 5 Apr (W)<br />
| [[Alice: Vehicle Control|Alice: adrive, astate, trajFollower]]<br />
| {{ncsbook|alice|App A}}; [http://gc.caltech.edu/wiki/index.php/Alice GCwiki]<br />
|-<br />
| 7 Apr* (F)<br />
| No class<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=3 | '''Real-time trajectory generation and receding horizon control (R. Murray)'''<br />
|-<br />
| 10 Apr (M)<br />
| [[NCS: Real-Time Trajectory Generation|Real-time trajectory generation]]<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 12 Apr* (W)<br />
| [[NCS: Receding Horizon Control|Receding horizon control]] (T. Keviczky)<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 14 Apr (F)<br />
| [[Alice: Path Planning|Alice: plannerModule]]<br />
| {{ncsbook|alice|App A}}; [http://grandchallenge.caltech.edu/wiki/images/b/b3/Thesis.pdf Kogan, 2005]<br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=3 | '''State estimation (H. Sandberg)'''<br />
|-<br />
| 17 Apr (M)<br />
| [[NCS: Kalman Filtering|Kalman filtering]]<br />
| {{ncsbook|estim|Ch 4}}; [http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf Welch and Bisop]<br />
|-<br />
| 19 Apr (W)<br />
| [[NCS: Moving Horizon Control|Moving horizon estimation]] <br />
| {{ncsbook|estim|Ch 4}}<br />
|-<br />
| 21 Apr (F) <br />
| [[Alice: State Estimation|Alice: estimModule]] (L. Cremean)<br />
| {{ncsbook|alice|App A}}<br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=3 | '''Packet-based estimation and control, I (B. Sinopoli)'''<br />
{{MWFrow|<br />
week=5|<br />
mondate=24 Apr*|montopic=|monreading=|<br />
weddate=26 Apr*|wedtopic=|wedreading=|<br />
fridate=28 Apr*|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=3 | '''Packet-based estimation and control, II (L. Shi, Y. Mostofi)'''<br />
{{MWFrow|<br />
week=6|<br />
mondate=1 May*|montopic=|monreading=|<br />
weddate=3 May|wedtopic=|wedreading=|<br />
fridate=5 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=3 | '''Distributed estimation and control (V. Gupta)'''<br />
{{MWFrow|<br />
week=7|<br />
mondate=8 May*|montopic=|monreading=|<br />
weddate=10 May*|wedtopic=|wedreading=|<br />
fridate=12 May |fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=3 | '''Cooperative control of multi-agent systems (Z. Jin, T. Keviczky)'''<br />
{{MWFrow|<br />
week=8|<br />
mondate=15 May|montopic=|monreading=|<br />
weddate=17 May*|wedtopic=|wedreading=|<br />
fridate=19 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=3 | '''Project Presentations (All)'''<br />
{{MWFrow|<br />
week=9|<br />
mondate=22 May|montopic=No class|monreading=|<br />
weddate=24 May|wedtopic=Project presentations|wedreading=|<br />
fridate=26 May|fritopic=Project presentations|frireading=|<br />
}}<br />
|}<br />
<br />
== Course Description ==<br />
<br />
Increases in fast and inexpensive computing and communications have enabled a new generation information-rich control systems that rely on multi-threaded networked execution, distributed optimization, adaptation and learning, and contingency management in increasingly sophisticated ways. This course will describe a framework for building such systems and lay out some of the challenges to control theory that must be addressed to enable systematic design and analysis. Two examples will be used to illustrate the results and to serve as testbeds for course projects: [[Alice]], an autonomous vehicle that competed in the 2005 DARPA Grand<br />
Challenge and [[RoboFlag]], a robotic version of capture the flag. Key features of these systems include highly sensory-driven, information rich feedback systems, higher levels of decision making for goal and contingency management, and multi-threaded, networked control architectures.<br />
<br />
== Course Administration ==<br />
<br />
This course is a special topics course in which advanced students will prepare and present much of the lecture material. There is no required homework and no midterm or final exam. Course grades will be based on a course project.<br />
<br />
== Course Project ==<br />
<br />
All students in the course will demonstrate their knowledge of the material by analyzing or implementing a networked control system algorithm. Two testbeds are available for use by the class:<br />
<br />
* <p> '''[[Alice]]''' - Alice is an autonomous vehicle that was built by [http://team.caltech.edu Caltech undergraduates] to compete in the 2005 DARPA Grand Challenge. It is fully equipped with multiple terrain sensing cameras and LADARS, two GPS units and an inertial measurement unit (IMU) for measuring position and orientation, and 10 CPUs of computing horsepower inteconnected by a 1 Gb/s ethernet network. A module software architecture allows new functionality to be implemented and tested with relative ease. Requires knowledge of C/C++ programming under linux.</p><br />
<br />
* <p> '''[[RoboFlag]]''' - RoboFlag is a robotic version of capture the flag in which teams of 6-8 robots with 1-2 humans compete against a like team. A high fidelity simulator is available that allow full simulation of the dynamics, sensing and communications subsystems, providing realistic operation. Features include limited bitrate communication channels, limited sensor range for detecting opposing robots, and a graphical user interface for human-in-the-loop operation. Required knowlege of C/C++ program under Windows.</p><br />
<br />
'''Project ideas''' (will be expanded during the term)<br />
* Benchmark the performance of different messaging protocols (eg, broadcast, UDP, TCP) for communicating the state and terrain data on Alice<br />
* Implement and analyze the effect of "shock absobers" (control buffers, state estimators) on RoboFlag<br />
* Implement state estimation and/or multi-description coding on Alice to handle lost packets of terrain data<br />
<br />
<span id=archive /><br />
<br />
[[Category:Courses]] [[Category:2005-06 Courses]]</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=CDS_270-2,_Spring_2006&diff=3483CDS 270-2, Spring 20062006-04-11T02:45:46Z<p>Sandberg: /* Course Schedule */</p>
<hr />
<div><table width="100%" cellspacing=0><br />
<tr valign=top><br />
<td rowspan=2 align=center> [[Image:citlogo.png|75px]]<br />
<td align=center><font color='blue' size='+2'>Networked Control Systems</font><br />
<td rowspan=2 align=center> [[Image:cdslogo.png|90px]]<br />
<tr valign=top><td align=center><font color='blue' size='+1'>Spring 2006</font><br />
</table><br />
<br />
<table align=right><tr><td>__TOC__</table><br />
<table cellspacing=0 cellpadding=0><br />
<tr valign=top><br />
<td width=60%><br />
* Instructor: [[User:Murray|Richard M. Murray]]<br />
* Co-instructors: [[User:Keviczky|Tamas Keviczky]], [[User:Mostofi|Yasi Mostofi]], [[User:Sandberg|Henrik Sandberg]], [[User:Sinopoli|Bruno Sinopoli]]<br />
<td align=center><br />
<table cellpadding=0 cellspacing=0><tr><td><br />
* [[Media:cds270-2_syllabus_sp06.pdf|Course syllabus]]<br />
* [http://listserv.cds.caltech.edu/mailman/listinfo/cds270 Course mailing list]<br />
* [[CDS 270: Information for Lecturers|Information for lecturers]]<br />
</table><br />
<tr><td colspan=2><br />
* Graduate instructors: Vijay Gupta, Zhipu Jin, Ling Shi, Demetri Spanos<br />
* Lectures: MWF 2-3 pm, 125 Steele<br />
</table><br />
<br />
== Course Schedule ==<br />
<br />
{| border=1 width=100%<br />
|-<br />
| Week || Date || Topic || Reading<br />
|-<br />
| align=center rowspan=5 | 1 <br />
| colspan=3 | '''Introduction to Networked Control Systems (R. Murray)'''<br />
|-<br />
| 27 Mar (M)<br />
| [[NCS: Introduction|Course overview, applications and administration]]<br />
| [[Media:cds270-2_syllabus_sp06.pdf|Syllabus]]; {{ncsbook|introduction|Ch 1}}<br />
|-<br />
| 29 Mar (W)<br />
| [[Alice: Introduction|Case study: Alice]]<br />
| [http://www.cds.caltech.edu/~murray/papers/2005t_cre+06-jfr.html Cremean et al, 2005]<br />
|-<br />
| colspan=3 | '''Networked embedded systems programming (R. Murray)'''<br />
|-<br />
| 31 Mar (F)<br />
| [[NCS: Message Transfer Systems|Message transfer systems: spread]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://portal.acm.org/citation.cfm?id=359563 Lamport, 1978]<br />
|-<br />
| align=center rowspan=3 | 2<br />
| 3 Apr (M)<br />
| [[NCS: Multi-Threaded Control Systems|Multi-threaded control systems: pthreads]]<br />
| {{ncsbook|embedded|Ch 2}}; [http://www.llnl.gov/computing/tutorials/pthreads Pthreads]<br />
|-<br />
| 5 Apr (W)<br />
| [[Alice: Vehicle Control|Alice: adrive, astate, trajFollower]]<br />
| {{ncsbook|alice|App A}}; [http://gc.caltech.edu/wiki/index.php/Alice GCwiki]<br />
|-<br />
| 7 Apr* (F)<br />
| No class<br />
| <br />
|-<br />
| align=center rowspan=4 | 3<br />
| colspan=3 | '''Real-time trajectory generation and receding horizon control (R. Murray)'''<br />
|-<br />
| 10 Apr (M)<br />
| [[NCS: Real-Time Trajectory Generation|Real-time trajectory generation]]<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 12 Apr* (W)<br />
| [[NCS: Receding Horizon Control|Receding horizon control]] (T. Keviczky)<br />
| {{ncsbook|trajgen|Ch 3}}<br />
|-<br />
| 14 Apr (F)<br />
| [[Alice: Path Planning|Alice: plannerModule]]<br />
| {{ncsbook|alice|App A}}; [http://grandchallenge.caltech.edu/wiki/images/b/b3/Thesis.pdf Kogan, 2005]<br />
|-<br />
| align=center rowspan=4 | 4<br />
| colspan=3 | '''State estimation (H. Sandberg)'''<br />
|-<br />
| 17 Apr (M)<br />
| [[NCS: State estimation|Kalman filtering]]<br />
| {{ncsbook|estim|Ch 4}}; [http://www.cs.unc.edu/~welch/media/pdf/kalman_intro.pdf Welch and Bisop]<br />
|-<br />
| 19 Apr (W)<br />
| [[NCS: State estimation|Moving horizon estimation]] <br />
| {{ncsbook|estim|Ch 4}}<br />
|-<br />
| 21 Apr (F) <br />
| [[Alice: State estimation|Alice: estimModule]] (L. Cremean)<br />
| {{ncsbook|alice|App A}}<br />
|-<br />
| align=center rowspan=4 | 5<br />
| colspan=3 | '''Packet-based estimation and control, I (B. Sinopoli)'''<br />
{{MWFrow|<br />
week=5|<br />
mondate=24 Apr*|montopic=|monreading=|<br />
weddate=26 Apr*|wedtopic=|wedreading=|<br />
fridate=28 Apr*|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 6<br />
| colspan=3 | '''Packet-based estimation and control, II (L. Shi, Y. Mostofi)'''<br />
{{MWFrow|<br />
week=6|<br />
mondate=1 May*|montopic=|monreading=|<br />
weddate=3 May|wedtopic=|wedreading=|<br />
fridate=5 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 7<br />
| colspan=3 | '''Distributed estimation and control (V. Gupta)'''<br />
{{MWFrow|<br />
week=7|<br />
mondate=8 May*|montopic=|monreading=|<br />
weddate=10 May*|wedtopic=|wedreading=|<br />
fridate=12 May |fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 8<br />
| colspan=3 | '''Cooperative control of multi-agent systems (Z. Jin, T. Keviczky)'''<br />
{{MWFrow|<br />
week=8|<br />
mondate=15 May|montopic=|monreading=|<br />
weddate=17 May*|wedtopic=|wedreading=|<br />
fridate=19 May|fritopic=|frireading=|<br />
}}<br />
|-<br />
| align=center rowspan=4 | 9<br />
| colspan=3 | '''Project Presentations (All)'''<br />
{{MWFrow|<br />
week=9|<br />
mondate=22 May|montopic=No class|monreading=|<br />
weddate=24 May|wedtopic=Project presentations|wedreading=|<br />
fridate=26 May|fritopic=Project presentations|frireading=|<br />
}}<br />
|}<br />
<br />
== Course Description ==<br />
<br />
Increases in fast and inexpensive computing and communications have enabled a new generation information-rich control systems that rely on multi-threaded networked execution, distributed optimization, adaptation and learning, and contingency management in increasingly sophisticated ways. This course will describe a framework for building such systems and lay out some of the challenges to control theory that must be addressed to enable systematic design and analysis. Two examples will be used to illustrate the results and to serve as testbeds for course projects: [[Alice]], an autonomous vehicle that competed in the 2005 DARPA Grand<br />
Challenge and [[RoboFlag]], a robotic version of capture the flag. Key features of these systems include highly sensory-driven, information rich feedback systems, higher levels of decision making for goal and contingency management, and multi-threaded, networked control architectures.<br />
<br />
== Course Administration ==<br />
<br />
This course is a special topics course in which advanced students will prepare and present much of the lecture material. There is no required homework and no midterm or final exam. Course grades will be based on a course project.<br />
<br />
== Course Project ==<br />
<br />
All students in the course will demonstrate their knowledge of the material by analyzing or implementing a networked control system algorithm. Two testbeds are available for use by the class:<br />
<br />
* <p> '''[[Alice]]''' - Alice is an autonomous vehicle that was built by [http://team.caltech.edu Caltech undergraduates] to compete in the 2005 DARPA Grand Challenge. It is fully equipped with multiple terrain sensing cameras and LADARS, two GPS units and an inertial measurement unit (IMU) for measuring position and orientation, and 10 CPUs of computing horsepower inteconnected by a 1 Gb/s ethernet network. A module software architecture allows new functionality to be implemented and tested with relative ease. Requires knowledge of C/C++ programming under linux.</p><br />
<br />
* <p> '''[[RoboFlag]]''' - RoboFlag is a robotic version of capture the flag in which teams of 6-8 robots with 1-2 humans compete against a like team. A high fidelity simulator is available that allow full simulation of the dynamics, sensing and communications subsystems, providing realistic operation. Features include limited bitrate communication channels, limited sensor range for detecting opposing robots, and a graphical user interface for human-in-the-loop operation. Required knowlege of C/C++ program under Windows.</p><br />
<br />
'''Project ideas''' (will be expanded during the term)<br />
* Benchmark the performance of different messaging protocols (eg, broadcast, UDP, TCP) for communicating the state and terrain data on Alice<br />
* Implement and analyze the effect of "shock absobers" (control buffers, state estimators) on RoboFlag<br />
* Implement state estimation and/or multi-description coding on Alice to handle lost packets of terrain data<br />
<br />
<span id=archive /><br />
<br />
[[Category:Courses]] [[Category:2005-06 Courses]]</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Stanford_Trip,_6-7_Apr_06&diff=3379Stanford Trip, 6-7 Apr 062006-04-03T17:31:21Z<p>Sandberg: /* Lodging */</p>
<hr />
<div>__NOTOC__The following people have sent e-mail saying they plan to attend:<br />
<table width=100%><br />
<tr valign=top><td width=33%><br />
* Arlene Cole-Rhodes<br />
* Jean-Charles Delvenne<br />
* Michael Epstein<br />
<td width=33%><br />
* Zhipu Jin<br />
* Richard Murray<br />
* Henrik Sandberg<br />
<td width=33%><br />
* Ling Shi<br />
* Fei Wang<br />
</table><br />
If your name isn't on this list, please send e-mail to Richard ASAP.<br />
<br />
== Travel to/from Stanford ==<br />
<br />
We will need to be at Stanford by about 9 am on Thursday morning. There are two choices for getting there: leaving Wed night and staying in a hotel, or leaving on Thursday morning (''very'' early) and driving straight to campus. Please edit one of the sections below and add your name to the appropriate list, so that we can make plan reservations:<br />
<br />
<table border=1 width=100%><br />
<tr valign=top><br />
<td width=50%><br />
=== Leaving Wednesday ===<br />
* Will leave Caltech around 6:30 pm, arriving at Stanford by 10 pm<br />
* Ling Shi<br />
* Fei Wang<br />
<td width=50%><br />
<br />
=== Leaving Thursday ===<br />
* Will leave Caltech at 6:00 am arriving at Stanford by 9 am<br />
* Richard Murray<br />
* Arlene Cole-Rhodes<br />
* Zhipu Jin<br />
* Michael Epstein<br />
* Henrik Sandberg<br />
</table><br />
<br />
== Lodging ==<br />
<br />
We'll share rooms when possible to save a bit of money. Please put your name down for one of the rooms below. Please try to share rooms with someone who is going the same day that you are.<br />
<br />
* Room 1: Richard (no roomate)<br />
* Room 2: Arlene (no roomate)<br />
* Room 3: Michael & Zhipu<br />
* Room 4: Henrik & Jean-Charles</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Stanford_Trip,_6-7_Apr_06&diff=3375Stanford Trip, 6-7 Apr 062006-04-03T16:57:08Z<p>Sandberg: /* Lodging */</p>
<hr />
<div>__NOTOC__The following people have sent e-mail saying they plan to attend:<br />
<table width=100%><br />
<tr valign=top><td width=33%><br />
* Arlene Cole-Rhodes<br />
* Jean-Charles Delvenne<br />
* Michael Epstein<br />
<td width=33%><br />
* Zhipu Jin<br />
* Richard Murray<br />
* Henrik Sandberg<br />
<td width=33%><br />
* Ling Shi<br />
* Fei Wang<br />
</table><br />
If your name isn't on this list, please send e-mail to Richard ASAP.<br />
<br />
== Travel to/from Stanford ==<br />
<br />
We will need to be at Stanford by about 9 am on Thursday morning. There are two choices for getting there: leaving Wed night and staying in a hotel, or leaving on Thursday morning (''very'' early) and driving straight to campus. Please edit one of the sections below and add your name to the appropriate list, so that we can make plan reservations:<br />
<br />
<table border=1 width=100%><br />
<tr valign=top><br />
<td width=50%><br />
=== Leaving Wednesday ===<br />
* Will leave Caltech around 6:30 pm, arriving at Stanford by 10 pm<br />
* Ling Shi<br />
* Fei Wang<br />
<td width=50%><br />
<br />
=== Leaving Thursday ===<br />
* Will leave Caltech at 6:00 am arriving at Stanford by 9 am<br />
* Richard Murray<br />
* Arlene Cole-Rhodes<br />
* Zhipu Jin<br />
* Michael Epstein<br />
* Henrik Sandberg<br />
</table><br />
<br />
== Lodging ==<br />
<br />
We'll share rooms when possible to save a bit of money. Please put your name down for one of the rooms below. Please try to share rooms with someone who is going the same day that you are.<br />
<br />
* Room 1: Richard (no roomate)<br />
* Room 2: Arlene (no roomate)<br />
* Room 3: Michael & Zhipu<br />
* Room 4: Henrik & ?</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Stanford_Trip,_6-7_Apr_06&diff=3373Stanford Trip, 6-7 Apr 062006-04-03T16:55:18Z<p>Sandberg: /* Lodging */</p>
<hr />
<div>__NOTOC__The following people have sent e-mail saying they plan to attend:<br />
<table width=100%><br />
<tr valign=top><td width=33%><br />
* Arlene Cole-Rhodes<br />
* Jean-Charles Delvenne<br />
* Michael Epstein<br />
<td width=33%><br />
* Zhipu Jin<br />
* Richard Murray<br />
* Henrik Sandberg<br />
<td width=33%><br />
* Ling Shi<br />
* Fei Wang<br />
</table><br />
If your name isn't on this list, please send e-mail to Richard ASAP.<br />
<br />
== Travel to/from Stanford ==<br />
<br />
We will need to be at Stanford by about 9 am on Thursday morning. There are two choices for getting there: leaving Wed night and staying in a hotel, or leaving on Thursday morning (''very'' early) and driving straight to campus. Please edit one of the sections below and add your name to the appropriate list, so that we can make plan reservations:<br />
<br />
<table border=1 width=100%><br />
<tr valign=top><br />
<td width=50%><br />
=== Leaving Wednesday ===<br />
* Will leave Caltech around 6:30 pm, arriving at Stanford by 10 pm<br />
* Ling Shi<br />
* Fei Wang<br />
<td width=50%><br />
<br />
=== Leaving Thursday ===<br />
* Will leave Caltech at 6:00 am arriving at Stanford by 9 am<br />
* Richard Murray<br />
* Arlene Cole-Rhodes<br />
* Zhipu Jin<br />
* Michael Epstein<br />
* Henrik Sandberg<br />
</table><br />
<br />
== Lodging ==<br />
<br />
We'll share rooms when possible to save a bit of money. Please put your name down for one of the rooms below. Please try to share rooms with someone who is going the same day that you are.<br />
<br />
* Room 1: Richard (no roomate)<br />
* Room 2: Arlene (no roomate)<br />
* Room 3: Michael & Zhipu<br />
* Room 4: Henrik</div>Sandberghttps://murray.cds.caltech.edu/index.php?title=Stanford_Trip,_6-7_Apr_06&diff=3372Stanford Trip, 6-7 Apr 062006-04-03T16:53:46Z<p>Sandberg: /* Leaving Thursday */</p>
<hr />
<div>__NOTOC__The following people have sent e-mail saying they plan to attend:<br />
<table width=100%><br />
<tr valign=top><td width=33%><br />
* Arlene Cole-Rhodes<br />
* Jean-Charles Delvenne<br />
* Michael Epstein<br />
<td width=33%><br />
* Zhipu Jin<br />
* Richard Murray<br />
* Henrik Sandberg<br />
<td width=33%><br />
* Ling Shi<br />
* Fei Wang<br />
</table><br />
If your name isn't on this list, please send e-mail to Richard ASAP.<br />
<br />
== Travel to/from Stanford ==<br />
<br />
We will need to be at Stanford by about 9 am on Thursday morning. There are two choices for getting there: leaving Wed night and staying in a hotel, or leaving on Thursday morning (''very'' early) and driving straight to campus. Please edit one of the sections below and add your name to the appropriate list, so that we can make plan reservations:<br />
<br />
<table border=1 width=100%><br />
<tr valign=top><br />
<td width=50%><br />
=== Leaving Wednesday ===<br />
* Will leave Caltech around 6:30 pm, arriving at Stanford by 10 pm<br />
* Ling Shi<br />
* Fei Wang<br />
<td width=50%><br />
<br />
=== Leaving Thursday ===<br />
* Will leave Caltech at 6:00 am arriving at Stanford by 9 am<br />
* Richard Murray<br />
* Arlene Cole-Rhodes<br />
* Zhipu Jin<br />
* Michael Epstein<br />
* Henrik Sandberg<br />
</table><br />
<br />
== Lodging ==<br />
<br />
We'll share rooms when possible to save a bit of money. Please put your name down for one of the rooms below. Please try to share rooms with someone who is going the same day that you are.<br />
<br />
* Room 1: Richard (no roomate)<br />
* Room 2: Arlene (no roomate)<br />
* Room 3: Michael & Zhipu<br />
* Room 4:</div>Sandberg