Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

• 成果类型: Article
• 署名作者: Williams, Alan; Krstic, Miroslav; Scheinker, Alexander
• 署名单位: University of California System; University of California San Diego; United States Department of Energy (DOE); Los Alamos National Laboratory
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2024.3469785
• 发表日期: 2025
• 页码: 1698-1713
• 关键词: safety; Heuristic algorithms; asymptotic stability; optimization; Filtering algorithms; Thermal stability; switches; CONVERGENCE; Approximation algorithms; Stability criteria; constrained optimization; extremum seeking (ES); safe control

摘要

We introduce a safe extremum-seeking algorithm that achieves the minimization of an unknown objective function while ensuring that an unknown, yet measured, control barrier function (CBF) remains above an arbitrarily small negative value for all time. In other words, practical safety is maintained during the entire period of convergence to the constrained extremum. Our design is based on quadratic program (QP) CBF style filters for safety, which is applied in an average and estimated sense. Using nonsmooth analysis tools, we guarantee semiglobal practical asymptotic (SPA) stability of the global constrained optimum, practical convergence to the safe set if starting in a condition violating the CBF, and practical safety for all time-semiglobally-if starting in safe set. The safety result of this article is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients that guarantee that such a small violation is not exceeded. This article outlines a set of sufficient conditions on the barrier and objective functions, and by way of a Lyapunov argument, we demonstrate that nonconvex constrained optimization problems can be solved. We present these results in the setting of a static map and a dynamical system. A simulation example illustrates the results.