Distributionally Robust Covariance Steering with Optimal Risk Allocation

TL;DR

This paper introduces a distributionally robust covariance steering method that optimally allocates risk under distributional ambiguity, ensuring robustness against uncertain state distributions in stochastic systems.

Contribution

It presents a novel distributionally robust risk allocation framework for covariance steering, combining a two-stage iterative approach with moment-based ambiguity sets.

Findings

The method provides solutions robust to arbitrary distributions within the ambiguity set.

Numerical simulations demonstrate the effectiveness of the proposed approach.

The framework enhances covariance steering robustness under distributional uncertainty.

Abstract

This article extends the optimal covariance steering (CS) problem for discrete time linear stochastic systems modeled using moment-based ambiguity sets. To hedge against the uncertainty in the state distributions while performing covariance steering, distributionally robust risk constraints are employed during the optimal allocation of the risk. Specifically, a distributionally robust iterative risk allocation (DR-IRA) formalism is used to solve the optimal risk allocation problem for the CS problem using a two-stage approach. The upper-stage of DR-IRA is a convex problem that optimizes the risk, while the lower-stage optimizes the controller with the new distributionally robust risk constraints. The proposed framework results in solutions that are robust against arbitrary distributions in the considered ambiguity set. Finally, we demonstrate our proposed approach using numerical simulations. Addressing the covariance steering problem through the lens of distributional robustness marks the novel contribution of this article.