An Observer-Based Extremum Seeking Controller Design for a Class of Second-Order Nonlinear Systems

In this letter, an extremum seeking controller (ESC) is designed for stabilization and output minimization for a class of second-order control-affine nonlinear systems. The main difficulty with such design lays in the fact that the relative degree between the measured output and the system’s input is two. As a result, the classical ESC approaches which use a high-pass filter for differentiation, are not suitable. We propose a perturbation-based controller in the feedback loop that utilizes a high-gain like observer with bounded derivatives of first and second-order. The closed-loop system is shown to be practically stable while maintaining the output in a small neighborhood of its optimum value. Simulation results demonstrate the effectiveness of the proposed approach.