Closed-Loop Finite-Time Analysis of Suboptimal Online Control

• 成果类型: Article
• 署名作者: Karapetyan, Aren; Balta, Efe C.; Iannelli, Andrea; Lygeros, John
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Stuttgart
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3539988
• 发表日期: 2025
• 页码: 5270-5285
• 关键词: costs; Benchmark testing; trajectory; Time-varying systems; Sufficient conditions; stability analysis; Real-time systems; optimal control; asymptotic stability; transient analysis; Nonlinear systems; optimization algorithms; Predictive control

摘要

Suboptimal methods in optimal control arise due to a limited computational budget, unknown system dynamics, or a short prediction window among other reasons. In this work, we study the transient closed-loop performance of such methods by providing finite-time suboptimality gap guarantees. We consider the control of discrete-time, nonlinear time-varying dynamical systems and establish sufficient conditions for such guarantees. These allow the control design to distribute a limited computational budget over a time horizon and estimate the on-the-go loss in performance due to suboptimality. We study exponential incremental input-to-state stabilizing policies and show that for nonlinear systems, under some mild conditions, this property is directly implied by exponential stability without further assumptions on global smoothness. The analysis is showcased on a suboptimal model predictive control use case.