Generalized Multi-Constraint Extremum Seeking

Abstract

We generalize the Safe Extremum Seeking algorithm to address the minimization of an unknown objective function subject to multiple unknown inequality and equality constraints, relying on recent results of gradient flow systems. These constraints may represent safety or other critical conditions. The proposed ES algorithm functions as a general nonlinear programming tool, offering practical maintenance of all constraints and semiglobal practical asymptotic stability, utilizing a Lyapunov argument on the penalty function and the set-valued Lie derivative. The efficacy of the algorithm is demonstrated on a 2D problem.