Jointly Optimal Quantization, Estimation, and Control of Hidden Markov Chains

Abstract

It is of interest to understand the tradeoff between the communication resource comsumption and the achievable system performance in networked control systems. In this paper we explore a general framework for trade-off analysis and decision making in such systems by studying joint quantization,estimation, and control of a hidden Markov chain. We first formulate the joint quantization and estimation problem, where vector quantization with variable-block length is considered. Dynamic programming (DP) is used to find the optimal quantization scheme that minimizes a weighted combination of the estimation error, the communication cost, and the delay due to block coding. The DP equation issolved numerically and simulation shows that this approach is able to capture the tradeoffs among competing objectives by adjusting the cost weights. We then study the joint quantization and control problem. An example problem is solved analytically, which provides interesting insight into the approach. In both the joint quantization/estimation problem and the joint quantization/control problem, we show that the separation principle holds. The approaches to solving these two problemsshare the same spirit, and can be combined and extended to accomodate more objectives.