Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties

We pose and solve an extremum seeking control problem for a class of nonlinear systems with unknown parameters. Extremum seeking controllers are developed to drive system states to the desired set-points that extremize the value of an objective function. The proposed adaptive extremum seeking controller is “inverse optimal” in the sense that it minimizes a meaningful cost function that incorporates penalty on both the performance error and control action. Simulation studies are provided to verify the effectiveness of the proposed approach.