Bayesian Optimization-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 adaptive approach, where we first design a robust nonlinear state feedback which renders the closed loop input-to-state stable (ISS). 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. We augment this robust ISS controller with a model-free learning algorithm to estimate the model uncertainties. We implement this method with a Bayesian optimization-based method called Gaussian Process Upper Confidence Bound (GP-UCB). The combination of the ISS feedback and the learning algorithms gives a learning-based modular indirect adaptive controller. We test the efficiency of this approach on a two-link robot manipulator example, under noisy measurements conditions.