 |
Center for Nonlinear Studies |
We discuss Safe Extremum Seeking (Safe ES), an algorithm designed to minimize an unknown yet measurable objective function while ensuring that an unknown, measurable constraint—referred to as a "Control Barrier Function" (CBF)—is approximately maintained throughout the trajectory. The measured CBF serves as a safety metric, ensuring that "practical safety" is achieved. Using nonsmooth analysis tools and a Lyapunov argument, 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 statement of safety 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. We further demonstrate the application of this algorithm to the 1-kilometer-long charged particle accelerator at the Los Alamos Neutron Science Center (LANSCE). In this context, our measured (but analytically unknown) safety metric is beam current, which must be maintained above a threshold to prevent damage to the machine or irradiation of components when tuning various accelerator parameters. The first example uses validated code to simulate the spot size tuning problem at pRad, optimizing the beam shape at 800 MeV. The second example shows an experimental tuning of the steering magnets in the low-energy transport region, performed during the 2023 maintenance period.
Host: Anatoly Zlotnik (T-5)