Attaining mean square boundedness of a marginally stable noisy linear system with a bounded control input

TL;DR

This paper develops simple, computable control policies that ensure bounded variance in noisy marginally stable linear systems, even with bounded control inputs and noise with bounded fourth moments.

Contribution

It introduces novel control policies that guarantee mean square boundedness for marginally stable systems under bounded control and noise conditions.

Findings

Control policies achieve bounded variance in the system.

Policies are simple and computationally feasible.

Applicable to systems with noise having bounded fourth moments.

Abstract

We construct control policies that ensure bounded variance of a noisy marginally stable linear system in closed-loop. It is assumed that the noise sequence is a mutually independent sequence of random vectors, enters the dynamics affinely, and has bounded fourth moment. The magnitude of the control is required to be of the order of the first moment of the noise, and the policies we obtain are simple and computable.