  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
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 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 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 (MDP).
