Optimal Covariance Control for Stochastic Systems Under Chance Constraints

TL;DR

This paper introduces a novel approach for optimal covariance control in stochastic systems with chance constraints, transforming the problem into a semidefinite program and demonstrating its effectiveness through simulations.

Contribution

It is the first to address covariance steering with probabilistic chance constraints and provides a semidefinite programming solution.

Findings

The approach successfully handles chance constraints in covariance steering.

The method is verified through numerical simulations.

Decoupling of mean and covariance is not possible with chance constraints.

Abstract

This work addresses the optimal covariance control problem for stochastic discrete-time linear time-varying systems subject to chance constraints. Covariance steering is a stochastic control problem to steer the system state Gaussian distribution to another Gaussian distribution while minimizing a cost function. To the best of our knowledge, covariance steering problems have never been discussed with probabilistic chance constraints although it is a natural extension. In this work, first we show that, unlike the case with no chance constraints, the covariance steering with chance constraints problem cannot decouple the mean and covariance steering sub-problems. Then we propose an approach to solve the covariance steering with chance constraints problem by converting it to a semidefinite programming problem. The proposed algorithm is verified using two simple numerical simulations.