Optimal tracking design of an MIMO linear system with quantization effects

This paper studies optimal design for a linear time-invariant (LTI) MIMO discrete-time networked feedback system in tracking a step signal. It is assumed that the outputs of the controller are quantized by logarithm quantization laws, respectively, and then transmitted through a communication network to the remote plant in the feedback system, whereas the quantization errors in all quantized signals are modeled as a product of a white noise with zero mean and the source signal respectively, the variances of the white noises are determined by the accuracies of the quantization laws. The tracking performance of the system we interested in is defined as the averaged energy of the error between the output of the plant and the reference input. Three problems are studied for the system: 1) For a set of given logarithm laws, how to design an optimal stabilizing controller for the closed-loop system in mean-square stability sense? 2) What is a minimal communication load to stabilize the networked feedback system in terms of the characteristics of the logarithm quantization laws? 3) For a set of given logarithm laws, how to design an optimal controller to achieve minimal tracking cost? We find that the problems 1 and 3 have a unique solution, respectively, and obtain an analytic solution for problem 2 when the plant is a minimum phase system. © 2011 IFAC.