Fixed-Time Gradient-Based Extremum Seeking

• Published in: 2020 American Control Conference (ACC) pp. 2838 - 2843
• Main Authors: Poveda, Jorge I., Krstic, Miroslav
• Format: Conference Proceeding
• Language: English
• Published: AACC 01-07-2020
• Subjects: Asymptotic stability; Convergence; Cost function; Heuristic algorithms; Stability analysis
• ISSN: 2378-5861
• DOI: 10.23919/ACC45564.2020.9148026

In this paper, we present the first averaging-based extremum seeking controller able to achieve semi-global practical fixed-time asymptotic stability in static maps, where by fixed-time asymptotic stability we mean convergence via a {\mathcal{K}}{\mathcal{L}} bound that has a finite-time convergence property with a uniformly bounded settling time. In general, this property cannot be achieved by standard smooth extremum seeking algorithms having a Lipschitz continuous average system. The extremum seeking dynamics are based on an underlying average system that is a perturbed version of a continuous gradient flow with prescribed finite-time convergence properties, recently studied in the literature. In order to study the stability properties of the ES dynamics, we make use of averaging tools for non-smooth dynamical systems, which allow us to link the {\mathcal{K}}{\mathcal{L}} bound of the average system with the {\mathcal{K}}{\mathcal{L}} bound that characterizes the convergence properties of the ES dynamics. Numerical simulations illustrate our results.