Stable Near-Optimal Control of Nonlinear Switched Discrete-Time Systems: An Optimistic Planning-Based Approach

• 成果类型: Article
• 署名作者: Granzotto, Mathieu; Postoyan, Romain; Busoniu, Lucian; Nesic, Dragan; Daafouz, Jamal
• 署名单位: Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); Technical University of Cluj Napoca; University of Melbourne
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3077873
• 发表日期: 2022
• 页码: 2298-2313
• 关键词: Algorithm design and analysis; asymptotic stability; cost function; Control system synthesis; dynamic programming; Lyapunov methods; Nonlinear systems; optimal control; Predictive control; stability analysis; Switched systems

摘要

Originating in the artificial intelligence literature, optimistic planning (OP) is an algorithm that generates near-optimal control inputs for generic nonlinear discrete-time systems whose input set is finite. This technique is, therefore, relevant for the near-optimal control of nonlinear switched systems for which the switching signal is the control, and no continuous input is present. However, OP exhibits several limitations, which prevent its desired application in a standard control engineering context, as it requires, for instance, that the stage cost takes values in [0.1], an unnatural prerequisite, and that the cost function is discounted. In this article, we modify OP to overcome these limitations, and we call the new algorithm OPmin. We then analyze OPmin under general stabilizability and detectability assumptions on the system and the stage cost. New near-optimality and performance guarantees for OPmin are derived, which have major advantages compared to those originally given for OP. We also prove that a system whose inputs are generated by OPmin in a receding-horizon fashion exhibits stability properties. As a result, OPmin provides a new tool for the near-optimal, stable control of nonlinear switched discrete-time systems for generic cost functions.