A Study on Optimal Random Dither Quantizers

Abstract

This paper addresses a problem of finding an optimal quantizer for control subject to discrete-valued signal constraints. The quantizers to be studied here are the random dither quantizers, which are given as the combination of a random number generator and a uniform quantizer. In this paper, we first show that the random dither quantizers whose random number is drawn from a uniform distribution is optimal for a class of linear systems. Furthermore, this fact is demonstrated by a numerical example.