Flexible-Step MPC for Switched Linear Systems With No Quadratic Common Lyapunov Function

• 成果类型: Article
• 署名作者: Furnsinn, Annika; Ebenbauer, Christian; Gharesifard, Bahman
• 署名单位: Queens University - Canada; RWTH Aachen University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3563122
• 发表日期: 2025
• 页码: 6316-6322
• 关键词: Lyapunov methods; optimal control; Linear systems; switches; STANDARDS; cost function; vectors; indexes; systematics; Stability criteria; Linear matrix inequalities (LMIs); Lyapunov function; predictive control for linear systems; Switched systems

摘要

In this article, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step model predictive control (MPC) scheme, recently introduced in (F & uuml;rnsinn et al., 2025), when restricted to the class of linear systems. Specifically, we show that a set of linear matrix inequalities (LMIs) can be used for this purpose, demonstrating its tractability. The main consequence of this LMI formulation is that, when combined with flexible-step MPC, we can effectively stabilize switched control systems, for which no quadratic common Lyapunov function exists.