LQG optimality and separation principle for general discrete time partially observed stochastic systems over finite capacity communication channels

Authors:
Charalambos D. Charalambous;Alireza Farhadi
Affiliations:
Electrical and Computer Engineering Department, University of Cyprus, 75 Kallipoleos Avenue, Nicosia, Cyprus and School of Information Technology and Engineering, University of Ottawa, 161 Louis P ...;School of Information Technology and Engineering, University of Ottawa, 800 King Edward Ave., Ottawa, Ontario, K1N 6N5, Canada
Venue:
Automatica (Journal of IFAC)
Year:
2008

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Abstract

This paper is concerned with control of stochastic systems subject to finite communication channel capacity. Necessary conditions for reconstruction and stability of system outputs are derived using the Information Transmission theorem and the Shannon lower bound. These conditions are expressed in terms of the Shannon entropy rate and the distortion measure employed to describe reconstruction and stability. The methodology is general, and hence it is applicable to a variety of systems. The results are applied to linear partially observed stochastic Gaussian controlled systems, when the channel is an Additive White Gaussian Noise (AWGN) channel. For such systems and channels, sufficient conditions are also derived by first showing that the Shannon lower bound is exactly equal to the rate distortion function, and then designing the encoder, decoder and controller which achieve the capacity of the channel. The conditions imposed are the standard detectability and stabilizability of Linear Quadratic Gaussian (LQG) theory, while a separation principle is shown between the design of the control and communication systems, without assuming knowledge of the control sequence at the encoder/decoder.