Optimal output feedback control of a class of linear systems with quasi-colored control-dependent multiplicative noise

TL;DR

This paper develops an optimal output feedback control method for discrete-time linear systems affected by a novel quasi-colored control-dependent multiplicative noise, applicable to networked systems with delays and erasures.

Contribution

It introduces a new noise model and derives a separation principle-based optimal control design using a modified algebraic Riccati equation.

Findings

The control design is explicitly solvable under certain system conditions.

The separation principle holds for the proposed control scheme.

Applications include networked systems with delays and erasure channels.

Abstract

This paper addresses the mean-square optimal control problem for \a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback. The noise under study is novel and shown to have advantage on modeling a class of network phenomena such as random transmission delays. The optimal output feedback controller is designed using an optimal mean-square state feedback gain and two observer gains, which are determined by the mean-square stabilizing solution to a modified algebraic Riccati equation (MARE), provided that the plant is minimum-phase and left-invertible. A necessary and sufficient condition for the existence of the stabilizing solution to the MARE is explicitly presented. It shows that the separation principle holds in a certain sense for the optimal control design of the work. The result is also applied to the optimal control problems in networked systems with random transmission delays and analog erasure channels, respectively.