Active probing for information in control systems with quantized state measurements: a minimum entropy approach

In this paper the effect of state quantization in scalar discrete-time linear control systems is studied by analyzing the system as a partially observed stochastic system. The problem of optimal state information gathering and filtering is investigated using information theoretic measures and formulating the state estimation problem as an entropy optimization problem. The active probing effect of the feedback control is thoroughly studied. Optimal feedback controls which minimize various types of entropy costs are determined, and it is shown that this problem is equivalent to an optimal control problem for a controlled Markov chain.