Perturbation-based Extremum Seeking Control Design for a Class of Nonlinear Systems

Abstract

In this paper, we try to address the problem of output (performance) function by applying the Perturbation-based Extremum Seeking Control (PESC) approach to the observer of the Single-Input Single-Output (SISO) nonlinear systems. In this work, PESC is applied so that the performance function can reach its maximum value. We apply tow controllers design that will take care of maximizing of the cost function. First controller is designed in the availability of full and unknown variables which are fed to the objective function, and the second controller is designed when the full state availability is removed, and these variables become known by applying the High Gain Observer (HGO) model to estimate the system variables. The construction of a seeking algorithm is used to drive the system variables and the observer output to the desired set-points that maximize the value of an objective (performance) function. In addition, Lyapunov's stability theorem and the perturbation theory including the averaging method are used in the design of the extremum seeking controller structure to check the stability of the system. Finally, the simulation results show the performance of the proposed procedures.