Adaptive extremum seeking control of a nonlinear system using backstepping technique

In common extremum seeking control methods, available knowledge of the system is disregarded. However, systems usually have known models with parametric uncertainties. Extremum seeking control for these systems have been solved recently, assuming output to be measurable or immeasurable. The problem for the case with immeasurable output has been solved only for a restricted class of nonlinear systems in which the cost function includes merely the states which are directly affected by control input. In the following, this class is extended to include wider range of nonlinear systems with parametric uncertainties. Using adaptive backstepping control technique, the cost function is drove to its extremum by forcing the states to follow their desired values. Simulation results demonstrate the efficiency of the proposed method.