Optimal Controller Synthesis and Dynamic Quantizer Switching for Linear-Quadratic-Gaussian Systems

In this article, we consider optimal controller synthesis of a quantized-feedback linear-quadratic-Gaussian (QF-LQG) system, where the measurements are to be quantized before being transmitted to the controller. The system is presented with several choices of quantizers, along with the cost of operating each quantizer. The objective is to jointly select the quantizers and the controller that would maintain an optimal balance between the control performance and quantization cost. Under certain assumptions, this problem can be decoupled into two optimization problems: one for optimal controller synthesis and the other for the 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 by solving a certain Markov decision process.