A Time-delay Approach for Extremum Seeking of Nonlinear Static Maps

This paper develops a constructive time-delay approach to averaging for gradient-based extremum seeking (ES) control of nonlinear static maps of non-quadratic form. Under the assumption that some prior knowledge of the nonlinear map with its derivatives is available, for the first time, we derive a quantitative analysis for ES close-loop systems with upper bounds on the tuning parameter that preserves the exponential stability and on the convergence error of extremum seeking. By transforming the ES system into a time-delay neutral type system with distributed delays, the developed method gives an accurate perturbed system of ES without employing any approximate calculation, and suggests a direct Lyapunov-Krasovskii approach in the form of linear matrix inequalities (LMIs), for the transformed time-delay plant to derive efficient stability conditions .