Control of jump linear systems over jump communication channels source channel matching approach
This presentation is the property of its rightful owner.
Sponsored Links
1 / 26

C. D. Charalambous Dep. of ECE University of Cyprus Nicosia, Cyprus PowerPoint PPT Presentation


  • 69 Views
  • Uploaded on
  • Presentation posted in: General

Control of Jump Linear Systems Over Jump Communication Channels – Source-Channel Matching Approach. S. Z. Denic Dep. of ECE University of Arizona Tucson. C. D. Charalambous Dep. of ECE University of Cyprus Nicosia, Cyprus. Control Over Communication Channel.

Download Presentation

C. D. Charalambous Dep. of ECE University of Cyprus Nicosia, Cyprus

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Control of jump linear systems over jump communication channels source channel matching approach

Control of Jump Linear Systems Over Jump Communication Channels – Source-Channel Matching Approach

S. Z. Denic

Dep. of ECE

University of Arizona

Tucson

C. D. Charalambous

Dep. of ECE

University of Cyprus

Nicosia, Cyprus


Control over communication channel

Control Over Communication Channel

  • Partially observed uncontrolled source is modulated by FSM chain; channel does not use feedback

  • Partially observed controlled source is modulated by FSM chain; channel uses feedback

Communication

Channel

Sink

Decoder

Dynamical

System

Encoder

Sensor

Collection and Transmission

of Information (Node 1)

Capacity Limited

Link

Reconstruction with

Distortion Error (Node 2)


Objectives

Objectives

  • Design encoders, decoders, controllers to achieve control and communication objectives

  • Establish a separation principle between communication and control system design


References

References

  • Tatikonda, Sahai, and Mitter, “Stochastic linear control over a communication channel,” 2004. (and Ph.D. Theses)

  • Nair, Dey, and Evans,“Communication limited stabilisability of jump Markov linear systems,” 2002.

  • Nair, Dey, and Evans, “Infimum data rates for stabilising Markov jump linear systems,” 2003.


Overview

Overview

  • Problem formulation

  • Necessary conditions for observability and stabilizability over causal communication channels

  • Source-channel matching

  • Conclusions


Problem formulation

Problem Formulation

  • Problem formulation

  • Information Measures

  • Necessary conditions for observability and stabilizability over

  • causal communication channels

  • Source-channel matching

  • Conclusions


Problem formulation1

Problem Formulation

  • Block diagram of control/communication system

Independent Crucial


Problem formulation2

Problem Formulation

  • Encoder, decoder, controller are causal

  • Communication channel with feedback

with feedback


Problem formulation3

Problem Formulation

Communication System Performance Measure

Definition: (Reconstruction in probability). Consider a control-communication system of Fig. 1. For a given δ ≥ 0 there exist an encoder and decoder (and control sequence) such that

Definition: (Reconstruction in r-th mean). Consider a control-communication system of Fig. 1. There exist an encoder and decoder (and control sequence) such that

where D ≥ 0 is finite.


Problem formulation4

Problem Formulation

Control System Performance Measures

Definition: (Stabilizability in probability). Consider a control-communication system of Fig. 1. For a given δ ≥ 0 there exist a controller, encoder and decoder such that

Definition: (Stabilizability in r-th mean). Consider a control-communication system of Fig. 1. There exist a controller, encoder and decoder such that

where D ≥ 0 is finite.


Information measures

Information Measures

Restricted Self-Information

  • Causality of Stochastic Kernels

  • Restricted Self-Mutual Information (RND)


Information measures1

Information Measures

Restricted Mutual-Information (Directed Information)

  • Expectation of Restricted self-Mutual Information

  • This is Directed Information [Massey]


Information measures2

Information Measures

Information Capacity and Rate Distortion

  • Information Channel Capacity

  • Information Rate distortion


Information measures3

Information Measures

Assumption:

FSM Chain is irreducible, Aperiodic, Homogeneous (Ergodic)

Standard Detectability and Stabilizability Conditions of Linear Quadratic Gaussian Theory Hold Uniformly over the States of the FSM Chain.


Necessary conditions for reconstruction and stabilizability over causal communication channels

Necessary conditions for reconstruction and stabilizability over causal communication channels

  • Problem formulation

  • Information Measures

  • Necessary conditions for reconstruction and stabilizability over

  • causal communication channels

  • Source-channel matching

  • Conclusions


Necessary conditions for reconstruction and stabilizability over causal communication channels1

Necessary conditions for reconstruction and stabilizability over causal communication channels

  • [Linder-Zamir 1994] Consider the following form of distortion measure

    , where

    Then, a lower bound for is given by

    where

    It follows

    and under some conditions, this lower bound is exact for


Necessary conditions for reconstruction and stabilizability over feedback communication channels

Necessary conditions for reconstruction and stabilizability over feedback communication channels

Application to the Jump System:


Necessary conditions for reconstruction and stabilizability over causal communication channels2

Necessary conditions for reconstruction and stabilizability over causal communication channels

  • A necessary condition for reconstruction and stabilizability in probability is given by


Necessary conditions for reconstruction and stabilizability over causal communication channels3

Necessary conditions for reconstruction and stabilizability over causal communication channels

is the covariance matrix of the Gaussian distribution which satisfies

A necessary condition for reconstruction and stabilizability in r-th mean is given by


Source channel matching

Source-Channel Matching

  • Problem formulation

  • Necessary conditions for observability and stabilizability over

  • causal communication channels

  • Source-channel matching

  • Conclusions


Source channel matching1

Source-Channel Matching

  • Consideruncontrolled system (U = 0).

  • Source signal processing. Define innovations process

  • Conditioned on the state S=s, K is orthogonal Gaussian process with

  • Compress the innovations process K and send it through the communication channel


Source channel matching2

Source-Channel Matching

  • Decoding.

  • Reconstruction with distortion D can be achieved by setting


Source channel matching3

Source-Channel Matching

  • Equivalent channel is given by

  • The transmission rate is given by

    where R(D) is the rate distortion between


Source channel matching4

Source-Channel Matching

  • Mean square error

  • The channel capacity

  • Since a sufficient condition for the reliable transmission is C>R(D) then

    is indeed compression


Source channel matching5

Source-Channel Matching

  • Controlled system

Y

Partially observed

dynamical system

(source)

Innovations

generator

K

AGN

Separation Can be Shown Between Control and Communication System Design; optimality of LGQ pay-off.

Mean square

estimator

Controller


Conclusions

Conclusions

  • Different Information Patters

  • Separation principle holds for Gaussian control and communication channels

  • Uncertain control systems and channels


  • Login