Extremum seeking-based indirect adaptive control for nonlinear systems with time-varying uncertainties

We study in this paper the problem of adaptive trajectory tracking control for nonlinear systems affine in the control with time-varying parametric uncertainties. We propose to use a modular approach, in the sense that we first design a robust nonlinear state feedback which renders the closed loop input to state stable (ISS) between an estimation error of the uncertain parameters and an output tracking error. Next, we complement this robust ISS controller with a model-free extremum seeking (ES) algorithm to estimate the time-varying model uncertainties. The combination of the ISS feedback and the ES algorithm gives an indirect adaptive controller. We show the efficiency of this approach on a two-link robot manipulator example.