Jointly Optimal LQG Quantization and Control Policies for Multi-Dimensional Systems

For controlled Rn-valued linear systems driven by Gaussian noise under quadratic cost criteria, we investigate the existence and the structure of optimal quantization and control policies. For fully observed and partially observed systems, we establish the global optimality of a class of predictive encoders and show that an optimal quantization policy exists, provided that the quantizers allowed are ones which have convex codecells. Furthermore, optimal control policies are linear in the conditional estimate of the state, and a form of separation of estimation and control holds.

[1]  R. Curry.  Estimation and Control with Quantized Measurements , 1970 .

[2]  J. T. Tou,et al.  Optimum Sampled-Data Systems with Quantized Control Signals , 1963, IEEE Transactions on Applications and Industry.

[3]  Minyue Fu,et al.  Lack of Separation Principle for Quantized Linear Quadratic Gaussian Control , 2012, IEEE Transactions on Automatic Control.

[4]  Tamás Linder,et al.  Optimization and convergence of observation channels in stochastic control , 2010, Proceedings of the 2011 American Control Conference.

[5]  V. Borkar.  White-noise representations in stochastic realization theory , 1993 .

[6]  Serdar Yüksel,et al.  On Optimal Causal Coding of Partially Observed Markov Sources in Single and Multiterminal Settings , 2010, IEEE Transactions on Information Theory.

[7]  Karl Henrik Johansson,et al.  Iterative Encoder-Controller Design for Feedback Control Over Noisy Channels , 2011, IEEE Transactions on Automatic Control.

[8]  Robin J. Evans,et al.  Feedback Control Under Data Rate Constraints: An Overview , 2007, Proceedings of the IEEE.

[9]  Tamer Basar,et al.  Stochastic Networked Control Systems , 2013 .

[10]  Sekhar Tatikonda,et al.  Stochastic linear control over a communication channel , 2004, IEEE Transactions on Automatic Control.

[11]  Tamer Basar,et al.  Stochastic Networked Control Systems: Stabilization and Optimization under Information Constraints , 2013 .

[12]  V. Borkar,et al.  LQG Control with Communication Constraints , 1997 .

[13]  Demosthenis Teneketzis,et al.  On the Structure of Optimal Real-Time Encoders and Decoders in Noisy Communication , 2006, IEEE Transactions on Information Theory.

[14]  Demosthenis Teneketzis,et al.  Optimal Performance of Networked Control Systems with Nonclassical Information Structures , 2009, SIAM J. Control. Optim..

[15]  Tamás Linder,et al.  On optimal zero-delay quantization of vector Markov sources , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[16]  Andrey V. Savkin,et al.  The problem of LQG optimal control via a limited capacity communication channel , 2004, Syst. Control. Lett..

[17]  H. Witsenhausen.  On the structure of real-time source coders , 1979, The Bell System Technical Journal.

[18]  T. Fischer,et al.  Optimal quantized control , 1982 .

[19]  Jean Walrand,et al.  Causal coding and control for Markov chains , 1983 .

[20]  Jean C. Walrand,et al.  Optimal causal coding - decoding problems , 1983, IEEE Trans. Inf. Theory.

[21]  Tamás Linder,et al.  Codecell convexity in optimal entropy-constrained vector quantization , 2003, IEEE Transactions on Information Theory.