  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.
