Learning-Based Modular Indirect Adaptive Control for a Class of Nonlinear Systems

We study in this paper the problem of adaptive trajectory tracking control for a class of nonlinear systems with parametric uncertainties. We propose to use a modular approach: we first design a robust nonlinear state feedback that renders the closed loop inputto-state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed-loop output tracking error. Next, we augment this robust ISS controller with a model-free learning algorithm to estimate the model uncertainties. We implement this method with two different learning approaches. The first one is a model-free multi-parametric extremum seeking (MES) method and the second is a Bayesian optimizationbased method called Gaussian Process Upper Confidence Bound (GPUCB). The combination of the ISS feedback and the learning algorithms gives a learning-based modular indirect adaptive controller. We show the efficiency of this approach on a two-link robot manipulator example.