Wasserstein Distributionally Robust Regret-Optimal Control under Partial Observability

TL;DR

This paper develops a Wasserstein distributionally robust regret-optimal control framework for partially observable systems, extending previous full-information solutions to handle measurement feedback and uncertainty.

Contribution

It introduces a tractable semi-definite programming approach for finite horizon partially observable DR-RO control, advancing robustness in uncertain environments.

Findings

The framework effectively handles partial observability and measurement noise.

Simulation results demonstrate improved robustness and performance.

The approach is computationally efficient for practical applications.

Abstract

This paper presents a framework for Wasserstein distributionally robust (DR) regret-optimal (RO) control in the context of partially observable systems. DR-RO control considers the regret in LQR cost between a causal and non-causal controller and aims to minimize the worst-case regret over all disturbances whose probability distribution is within a certain Wasserstein-2 ball of a nominal distribution. Our work builds upon the full-information DR-RO problem that was introduced and solved in Yan et al., 2023, and extends it to handle partial observability and measurement-feedback (MF). We solve the finite horizon partially observable DR-RO and show that it reduces to a tractable semi-definite program whose size is proportional to the time horizon. Through simulations, the effectiveness and performance of the framework are demonstrated, showcasing its practical relevance to real-world control systems. The proposed approach enables robust control decisions, enhances system performance in uncertain and partially observable environments, and provides resilience against measurement noise and model discrepancies.