Robust Adaptive Extremum Seeking Control Without Persistence of Excitation: Theory to Experiment

Abstract

In this article, we develop a novel adaptive extremum-seeking control (AdESC) algorithm with robustness guarantees and without persistence of excitation (PE). Specifically, this builds on a proportional-integral (PI)-like parameter estimator. A zeroth-order optimization framework is used, where the optimizer/agent can only query the numerical value of the cost function at the current coordinate given an unmodeled bounded disturbance. Since parameter estimation plays a decisive role in the stability and convergence properties of AdESC algorithm, it is also well established in the existing literature that to ensure parameter convergence a stringent PE condition is required. Here, we eliminate the need for a stringent PE condition by utilizing a novel set of weighted integral filter dynamics, while ensuring sufficient richness using a milder condition, called initial excitation (IE). Moreover, to validate the robustness guarantees towards unmodeled bounded disturbance, a detailed Lyapunov function based analysis is performed to establish the closed-loop stability and convergence in the form of uniform ultimate boundedness (UUB). Furthermore, an experimental study using a unicycle wheeled mobile robot (WMR) is carried out as a proof-of-concept considering disturbance and disturbance-free scenarios.