Computationally Efficient Covariance Steering for Systems Subject to Parametric Disturbances and Chance Constraints

TL;DR

This paper presents a computationally efficient convex approximation method for covariance steering in discrete-time linear systems with uncertainties and chance constraints, enabling practical control solutions.

Contribution

It introduces a convex approximation approach that simplifies the complex covariance steering problem under uncertainties and chance constraints.

Findings

The convex approximation provides a valid solution to the original problem.

The method effectively handles parametric disturbances and chance constraints.

The approach is computationally efficient and tractable.

Abstract

This work investigates the finite-horizon optimal covariance steering problem for discrete-time linear systems subject to both additive and multiplicative uncertainties as well as state and input chance constraints. In particular, a tractable convex approximation of the optimal covariance steering problem is developed by tightening the chance constraints and by introducing a suitable change of variables. The solution of the convex approximation is shown to be a valid (albeit potentially suboptimal) solution to the original chance-constrained covariance steering problem.