# Difference between revisions of "NCS: Packet-based Control: the TCP case"

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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 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 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. | ||

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== 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 --> | <!-- 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:L5-2_packet_based_control_slides.pdf |Lecture: TCP Packet-based Control slides]] |

+ | * [[Media:L5-2_packet_based_control.pdf |Lecture: TCP/UDP Packet-based Control notes]], | ||

For this lecture consider pages 57-71. | For this lecture consider pages 57-71. | ||

## Latest revision as of 00:44, 7 May 2006

Prev: Packet-based Estimation | Course Home | Next: Packet-based control UDP |

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.

## Lecture Materials

For this lecture consider pages 57-71.

## Reading

Optimal Control with Unreliable Communication: the TCP Case, B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla and S. Sastry. This is the paper where we published the results contained in the thesis

## Additional Resources

- 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.

Dynamic Programming and Optimal Control, by D. Bertsekas.

Neuro-Dynamic Programming, by D. Bertsekas and J. Tsitsiklis.