On the Design of Active Learning Controllers for Linear Systems with Quantized State Measurements

In this paper, we study the effect of state (or output) quantization in scalar discrete-time linear control systems by regarding the quantized state as a partial observation of the true state rather than an approximation. With this point of view, the quantized system is analyzed as a partially observed stochastic system and the problem of optimal state information gathering-from the history of the quantized output is investigated. It is shown that this problem is equivalent to an optimal control problem for a controlled Markov chain.