Extremum Seeking-based Indirect Adaptive Control for Nonlinear Systems with State and Time-Dependent Uncertainties

We study in this paper the problem of adaptive trajectory tracking for nonlinear systems affine in the control with bounded state-dependent and time-dependent 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 multiparametric extremum seeking (MES) algorithm to estimate the model uncertainties. The combination of the ISS feedback and the MES algorithm gives an indirect adaptive controller. We show the efficiency of this approach on a two-link robot manipulator example.