Wasserstein Distributionally Robust Regret-Optimal Control under Partial Observability

Joudi Hajar; Taylan Kargin; Babak Hassibi

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arXiv · 2307.04966

Wasserstein Distributionally Robust Regret-Optimal Control under Partial Observability

Joudi Hajar·Taylan Kargin·Babak Hassibi

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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.

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BibTeX RIS

Joudi Hajar, Taylan Kargin, Babak Hassibi. 2023-07-11. Wasserstein Distributionally Robust Regret-Optimal Control under Partial Observability. https://arxiv.org/abs/2307.04966

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