Optimal decentralized sigma-delta modulators for quantized feedback control

Abstract

This paper addresses a problem of designing decentralized sigma-delta modulators for quantized control, i.e., feedback control subject to quantized signal constraints. The sigma-delta modulators to be considered here have a limited information structure so as to be implemented in a decentralized manner, which poses a challenging design problem. We first analytically derive a solution to the problem such that the resulting quantized feedback system optimally approximates the corresponding unquantized system. Next, the performance is demonstrated by a numerical simulation and an experiment for the stabilization problem of a seesaw-cart system.