Learn and Control While Switching: Guaranteed Stability and Sublinear Regret

• 成果类型: Article
• 署名作者: Chekan, Jafar Abbaszadeh; Langbort, Cedric
• 署名单位: University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3440348
• 发表日期: 2024
• 页码: 8433-8448
• 关键词: Switches; control systems; actuators; Ellipsoids; Heuristic algorithms; Switched systems; Numerical stability; Overactuated system; regret; Reinforcement Learning; switched system

摘要

Overactuated systems often make it possible to achieve specific performances by switching between different subsets of actuators. However, when the system parameters are unknown, transferring authority to different subsets of actuators is challenging due to stability and performance efficiency concerns. This article presents an efficient algorithm to tackle the so-called learn and control while switching between different actuating modes problem in the linear quadratic setting. Our proposed strategy is constructed upon optimism in the face of uncertainty (OFU)-based algorithm equipped with a projection toolbox to keep the algorithm efficient, regretwise. Along the way, we derive an optimum duration for the warm-up phase, thanks to the existence of a stabilizing neighborhood. The stability of the switched system is also guaranteed by designing a minimum average dwell time. The proposed strategy is proved to have a regret bound of $\mathcal {O}(ns\sqrt{T})$ in horizon $T$ with $(ns)$ number of switches, provably outperforming naively applying the basic OFU algorithm.