A General Framework for Learning-Based Distributionally Robust MPC of Markov Jump Systems

• 成果类型: Article
• 署名作者: Schuurmans, Mathijs; Patrinos, Panagiotis
• 署名单位: KU Leuven
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3237999
• 发表日期: 2023
• 页码: 2950-2965
• 关键词: Markov processes; optimization; control systems; stability analysis; optimal control; Learning systems; safety; Predictive control; Robustness; Statistical learning

摘要

In this article, we present a data-driven learning model predictive control (MPC) scheme for chance-constrained Markov jump systems with unknown switching probabilities. Using samples of the underlying Markov chain, ambiguity sets of transition probabilities are estimated, which include the true conditional probability distributions with high probability. These sets are updated online and used to formulate a time-varying, risk-averse optimal control problem. We prove recursive feasibility of the resulting MPC scheme and show that the original chance constraints remain satisfied at every time step. Furthermore, we show that under sufficient decrease of the confidence levels, the resulting MPC scheme renders the closed-loop system mean-square stable with respect to the true-but-unknown distributions, while remaining less conservative than a fully robust approach. Finally, we show that the data-driven value function of the learning MPC converges from above to its nominal counterpart as the sample size grows to infinity. We illustrate our approach on a numerical example.