Convex optimization for finite horizon robust covariance control of linear stochastic systems

TL;DR

This paper develops a convex optimization-based method for designing robust control policies for linear stochastic systems with uncertain disturbances, ensuring specified performance criteria over a finite horizon.

Contribution

It introduces a tractable convex programming approach to robust covariance control under ellitopic uncertainty sets for partially observable linear systems.

Findings

The proposed method guarantees performance specifications.

The control design is computationally efficient.

Numerical example demonstrates effectiveness.

Abstract

This work addresses the finite-horizon robust covariance control problem for discrete-time, partially observable, linear system affected by random zero mean noise and deterministic but unknown disturbances restricted to lie in what is called ellitopic uncertainty set (e.g., finite intersection of centered at the origin ellipsoids/elliptic cylinders). Performance specifications are imposed on the random state-control trajectory via averaged convex quadratic inequalities, linear inequalities on the mean, as well as pre-specified upper bounds on the covariance matrix. For this problem we develop a computationally tractable procedure for designing affine control policies, in the sense that the parameters of the policy that guarantees the aforementioned performance specifications are obtained as solutions to an explicit convex program. Our theoretical findings are illustrated by a numerical example.