Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

Williams, Alan Brian; Krstic, Miroslav; Scheinker, Alexander

doi:10.1109/tac.2024.3469785

Title: Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

Journal Article · 27 September 2024 · IEEE Transactions on Automatic Control

DOI: https://doi.org/10.1109/tac.2024.3469785 · OSTI ID:2478087

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University of California, San Diego, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
University of California, San Diego, CA (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

We introduce a safe extremum-seeking (Safe ES) algorithm which 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 the paper is analogous with modern notions of SPA stability, guaranteeing that, for any small violation of safety, there exist design coefficients which guarantee that such a small violation is not exceeded. The paper 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.

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Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 2478087

Report Number(s):: LA-UR--24-23906

Journal Information:: IEEE Transactions on Automatic Control, Journal Name: IEEE Transactions on Automatic Control Journal Issue: 3 Vol. 70; ISSN 0018-9286

Publisher:: IEEECopyright Statement

Country of Publication:: United States

Language:: English

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Title: Semiglobal Safety-Filtered Extremum Seeking With Unknown CBFs

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