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- W4353082010 abstract "To address the issue of inaccurate distributions in practical stochastic systems, a minimax linear-quadratic control method is proposed using the Wasserstein metric. Our method aims to construct a control policy that is robust against errors in an empirical distribution of underlying uncertainty, by adopting an adversary that selects the worst-case distribution. The opponent receives a Wasserstein penalty proportional to the amount of deviation from the empirical distribution. A closed-form expression of the finite-horizon optimal policy pair is derived using a Riccati equation. The result is then extended to the infinite-horizon average cost setting by identifying conditions under which the Riccati recursion converges to the unique positive semi-definite solution to an algebraic Riccati equation. Our method is shown to possess several salient features including closed-loop stability, and an out-of-sample performance guarantee. We also discuss how to optimize the penalty parameter for enhancing the distributional robustness of our control policy. Last but not least, a theoretical connection to the classical $H_infty$-method is identified from the perspective of distributional robustness." @default.
- W4353082010 created "2023-03-23" @default.
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- W4353082010 date "2021-02-25" @default.
- W4353082010 modified "2023-10-18" @default.
- W4353082010 title "Distributional robustness in minimax linear quadratic control with Wasserstein distance" @default.
- W4353082010 doi "https://doi.org/10.48550/arxiv.2102.12715" @default.
- W4353082010 hasPublicationYear "2021" @default.
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