Jump LQR Systems With Unknown Transition Probabilities

• 成果类型: Article
• 署名作者: Tzortzis, Ioannis; Charalambous, Charalambos D.; Hadjicostis, Christoforos N.
• 署名单位: University of Cyprus
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3013844
• 发表日期: 2021
• 页码: 2693-2708
• 关键词: Probability distribution; uncertainty; Markov processes; Robustness; measurement; control systems; dynamic programming; minimax optimization; nonhomogeneous Markov jump linear systems; robust linear quadratic regulator; uncertain; ambiguous transition probabilities

摘要

This article develops a robust linear quadratic regulator (LQR) approach applicable to nonhomogeneous Markov jump linear systems with uncertain transition probability distributions. The stochastic control problem is investigated under two equivalent formulations, using i) minimax optimization theory, and ii) a total variation distance metric as a tool for codifying the level of uncertainty of the jump process. By following a dynamic programming approach, a robust optimal controller is derived, which in addition to minimizing the quadratic cost, it also restricts the influence of uncertainty. A solution procedure for the LQR problem is also proposed, and an illustrative example is presented. Numerical results indicate the applicability and effectiveness of the proposed approach.