Difference between revisions of "Packet-based Control with Norm Bounded Uncertainties"

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<!-- 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 -->
<!-- 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 -->
In this lecture, we study the effect of data loss on the performance of the Kalman filter for discrete-time linear systems. Observations are lost according to a bernoulli independent process, modeling this way the presence of a lossy networks between the sensors and the estimator. We first prove that the Kalman filter is still optimal in this new scenario.
In this lecture, we study the main issues with a packet-based control system and explore the frequently used models for such systems. In particular, we study the effect of packet drops and finite data rate on the system stability. We shall show that there are tradeoffs between packet drop rate, network data rate and system uncertainty levels for the closed loop system.
We then provide asymptotic results on the performance of the filter. In particular, we show that a transition from boundedness to instability arises if the arrival probability is lower that a critical value, that depends on the unstable eigenvalues of the system.


== Lecture Materials ==
== Lecture Materials ==
<!-- 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 -->
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<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] -->
<!-- Sample lecture link: * [[Media:L1-1_Intro.pdf|Lecture: Networked Control Systems: Course Overview]] -->
* [[Media:L5-1_packet_based_estimation.pdf |Lecture: Packet-based Estimation]]
* [[Media:270_2 Lecture_Ling.pdf |Lecture: Packet-based Estimation and Control II ]]


== Reading ==
== Reading ==
* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/tacs04.pdf Kalman Filtering with Intermittent Observations], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. Jordan and S. Sastry. This is the paper where all the proofs reside. Below I posted Chapter 3 of my thesis, which is essentially the same, but the notation is more consistent with the next two lectures.</p>
* <p>[http://www.cds.caltech.edu/~shiling/acc06final.pdf Networked Control Systems with Norm Bounded Uncertainties: A Stability Analysis], Ling Shi, Michael Epstein and Richard M.Murray. The first half of the lecture is based on this paper.</p>


* <p>[http://robotics.eecs.berkeley.edu/~sinopoli/NCS_class/optimal_estimation_lossy.pdf Optimal Estimation in Lossy Networks] This is chapter 3 of my thesis. Content is almost the same as the paper above, but notation is slightly modified to be consistent with the control part.</p>
* <p>[http://www.cds.caltech.edu/~shiling/mtns06.pdf Towards Robust Control Over a Packet Dropping Network], Ling Shi, Michael Epstein and Richard M.Murray. The second half of the lecture is based on this paper.</p>




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== Additional Resources ==
== Additional Resources ==
* <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>
* <p>[http://en.wikipedia.org/wiki/Almost_surely Almost Sure in Probability Theory]. This is a pretty good introduction to the notion of "Almost Surely" from wikipedia.</p>


* <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>
In case you want to explore more besides these two papers, you can find related papers through our references. And you are welcome to talk to either me or Michael for possible project ideas.  


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Latest revision as of 17:11, 29 April 2006

Prev: Packet-based Control: UDP Case Course Home Next: Estimation Over Wireless Links

In this lecture, we study the main issues with a packet-based control system and explore the frequently used models for such systems. In particular, we study the effect of packet drops and finite data rate on the system stability. We shall show that there are tradeoffs between packet drop rate, network data rate and system uncertainty levels for the closed loop system.

Lecture Materials

Reading


Additional Resources

In case you want to explore more besides these two papers, you can find related papers through our references. And you are welcome to talk to either me or Michael for possible project ideas.