Extremum seeking control via monitoring function and time-scaling for plants of arbitrary relative degree

An output-feedback variable-structure based extremum seeking controller was recently introduced for nonlinear uncertain systems by using a monitoring function. The class of systems considered was restricted to the relative degree one case. In this paper, generalization is achieved to include more general dynamics with arbitrary relative degree, uncertain parameters and order. Global stability properties of the closed-loop system and exponential convergence to a neighborhood of the desired extremum are proved. The main contribution of this paper is to develop a time-scaling procedure to essentially reduce the analysis and control design to that of a relative degree one case. Simulation results illustrate the performance of the proposed extremum seeking control algorithm in different time scales.