A Novel Extremum Seeking Control to Enhance Convergence and Robustness in the Presence of Nonlinear Dynamic Sensors

Abstract

This paper focuses on optimizing an unknown cost function through extremum seeking (ES) control in the presence of a slow nonlinear dynamic sensor responsible for measuring the cost. In contrast to traditional perturbation-based ES control, which often suffers from sluggish convergence, the proposed method eliminates the time-scale separation between sensor dynamics and ES control by using the relative degree of the nonlinear sensor system. To improve the convergence rate, the authors incorporate high-frequency dither signals and a differentiator. To enhance the robustness with the existence of rapid disturbances, an off-the-shelf linear high-gain differentiator is applied. The first result demonstrates that, for any desired convergence rate, with properly tuned parameters for the proposed ES algorithm, the input of the cost function can converge to an arbitrarily small neighborhood of the optimal solution, starting from any initial condition within any given compact set. Furthermore, the second result shows the robustness of the proposed ES control in the presence of sufficiently fast, zero-mean periodic disturbances. Simulation results substantiate these theoretical findings.