Sinopoli at 00:50, 7 May 2006

2006-05-07T00:50:22Z

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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:L5-3_packet_based_control_slides.pdf \|Lecture: UDP Packet-based Control slides]]		* [[Media:L5-3_packet_based_control_slides.pdf \|Lecture: UDP Packet-based Control slides]]
	* [[Media:L5-2_packet_based_control.pdf \|Lecture: TCP/UDP Packet-based Control]],		* [[Media:L5-2_packet_based_control.pdf \|Lecture: TCP/UDP Packet-based Control]]
	For this lecture consider pages 71-88.		For this lecture consider pages 71-88.

Sinopoli at 00:47, 7 May 2006

2006-05-07T00:47:35Z

← Older revision		Revision as of 00:47, 7 May 2006
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	<!-- 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 -->		<!-- 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 -->
	<!-- 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:L5-2_packet_based_control.pdf \|Lecture: Packet-based Control]],		* [[Media:L5-3_packet_based_control_slides.pdf \|Lecture: UDP Packet-based Control slides]]
			* [[Media:L5-2_packet_based_control.pdf \|Lecture: TCP/UDP Packet-based Control]],
	For this lecture consider pages 71-88.		For this lecture consider pages 71-88.

Sinopoli at 07:54, 28 April 2006

2006-04-28T07:54:30Z

New page

{{cds270-2 header}} 


In this lecture we consider the Linear Quadratic Gaussian (LQG) optimal control problem in the discrete time setting and when data loss may occur between the sensors and the estimation-control unit and between the latter and the actuation points. We focus on the case where the arrival of the control packet is acknowledged at the receiving actuator, as it happens with the common Transfer Control Protocol (TCP). We start by showing that the separation principle holds. Additionally, we can prove that the optimal LQG control is a linear function of the state. Finally, building upon the results shown in the previous lecture on estimation with unreliable communication, we show the existence of critical arrival probabilities below which the optimal controller fails to stabilize the system. This is done by providing analytic upper and lower bounds on the cost functional.
In the previous lectures we showed that, for protocols where
packets are acknowledged at the receiver (e.g.\ TCP type
protocols), the separation principle holds. Moreover, the optimal
LQG control is a linear function of the state. Finally, we showed the existence of critical arrival
probabilities below which the optimal controller fails to
stabilize the system. In this lecture we focus on UDP-like protocols. It turns out that when there is no feedback on whether a control packet has been delivered or not
(e.g. UDP type protocols), the LQG optimal controller is in
general nonlinear function of the information state. In the particular case where there is no measurement noise and the observation matrix C is invertible, we are able to show that the optimal controller is again linear, even if the separation principle still doesn't hold.
Necessary conditions on the arrival probabilities for state boundedness are provided.
== Lecture Materials ==


* [[Media:L5-2_packet_based_control.pdf |Lecture: Packet-based Control]],
For this lecture consider pages 71-88.

== Reading ==
* [http://robotics.eecs.berkeley.edu/~sinopoli/Sinopoli_ifac.pdf LQG Control with Missing Observation and Control Packets], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. Ifac 05

* [http://robotics.eecs.berkeley.edu/~sinopoli/cdc05.pdf An LQG Optimal Linear Controller for Control Systems with Packet Losses], B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. CDC 05



== Additional Resources ==

* [[Media:Nilsson_thesis_98.pdf | Real-Time Control Systems with Delays]], by Johan Nilsson, PhD Thesis.

==Books==
* Stochastic Systems: Estimation, Identification and Adaptive Control, by P.R. Kumar, P. Varaiya, Prentice Hall, 1986. Difficult to find (Richard has a copy though). Even if it is not the most user friendly reading, chapters 6 to 8 contain a good reference for dynamic programming and LQG control.

* [http://www.amazon.com/gp/product/1886529086/qid=1146074615/sr=2-2/ref=pd_bbs_b_2_2/103-1985563-9207029?s=books&v=glance&n=283155 Dynamic Programming and Optimal Control], by D. Bertsekas. 

* [http://www.amazon.com/gp/product/1886529108/qid=1146074615/sr=1-9/ref=sr_1_9/103-1985563-9207029?s=books&v=glance&n=283155 Neuro-Dynamic Programming], by D. Bertsekas and J. Tsitsiklis.

NCS: Packet-based Control: the UDP case - Revision history

Sinopoli at 00:50, 7 May 2006

Sinopoli at 00:47, 7 May 2006

Sinopoli at 07:54, 28 April 2006