Optimal Controller and Quantizer Selection for Partially Observable Linear-Quadratic-Gaussian Systems

In networked control systems, often the sensory signals are quantized before being transmitted to the controller.Consequently, performance is affected by the coarseness of this quantization process. Modern communication technologies allow users to obtain resolution-varying quantized measurements based on the prices paid. In this paper,we consider optimal controller synthesis of a partially observed Quantized-Feedback Linear-Quadratic-Gaussian (QF-LQG) system, where the measurements are to be quantized before being sent to the controller. The system is presented with several choices of quantizers, along with the cost of using each quantizer. The objective is to jointly select the quantizers and the controller that would maintain an optimal balance between control performance and quantization cost. Under the assumption of quantizing the innovation signal, this problem can be decoupled into two optimization problems: one for optimal controller synthesis, and the other for optimal quantizer selection. We show that, similarly to the classical LQG problem, the optimal controller synthesis subproblem is characterized by Riccati equations. On the other hand, the optimal quantizer selection policy is found offline by solving a linear program (LP).