Abstract:

We present in this chapter some recent results on learning-based adaptive control for nonlinear systems. We first study the problem of adaptive trajectory tracking for nonlinear systems, and show that for the class of nonlinear systems with parametric uncertainties which can be rendered integral Input-to-State stable w.r.t. the parameter estimation error, that it is possible to merge together the integral Input-to-State stabilizing feedback controller and a model-free extremum seeking (ES) algorithm to realize a learning-based adaptive controller. We investigate the performance of this approach in term of tracking errors upper-bounds, for two different ES algorithms. Next, we propose a learning-based approach to auto-tune the feedback gains for nonlinear stabilizing controllers.