期刊
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
卷 66, 期 8, 页码 3863-3870出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2020.3030884
关键词
Probability distribution; Robust control; Stochastic processes; Optimal control; Aerospace electronics; Optimization; Probabilistic logic; Dynamic programming (DP); optimal control; optimization; probability distribution; robustness; stochastic systems
资金
- NSF [ECCS-1708906]
- Creative-Pioneering Researchers Program through SNU
- National Research Foundation of Korea - MSIT [2020R1C1C1009766]
- Samsung Electronics
- National Research Foundation of Korea [2020R1C1C1009766] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
This article investigates the problem of control policy robustness and proposes a dynamic programming solution based on Wasserstein distribution. The study shows that the contraction property of Bellman operators can extend single-stage performance guarantees to multistage guarantees.
Standard stochastic control methods assume that the probability distribution of uncertain variables is available. Unfortunately, in practice, obtaining accurate distribution information is a challenging task. To resolve this issue, in this article we investigate the problem of designing a control policy that is robust against errors in the empirical distribution obtained from data. This problem can be formulated as a two-player zero-sum dynamic game problem, where the action space of the adversarial player is a Wasserstein ball centered at the empirical distribution. A dynamic programming solution is provided exploiting the reformulation techniques for Wasserstein distributionally robust optimization. We show that the contraction property of associated Bellman operators extends a single-stage out-of-sample performance guarantee, obtained using a measure concentration inequality, to the corresponding multistage guarantee without any degradation in the confidence level. Furthermore, we characterize an explicit form of the optimal control policy and the worst-case distribution policy for linear-quadratic problems with Wasserstein penalty.
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