We study in this paper the problem of adaptive trajectory tracking controlfor a class of nonlinear systems with parametric uncertainties. We propose touse a modular approach, where we first design a robust nonlinear state feedbackwhich renders the closed loop input-to-state stable (ISS), where the input isconsidered to be the estimation error of the uncertain parameters, and thestate is considered to be the closed-loop output tracking error. Next, weaugment this robust ISS controller with a model-free learning algorithm toestimate the model uncertainties. We implement this method with two differentlearning approaches. The first one is a model-free multi-parametric extremumseeking (MES) method and the second is a Bayesian optimization-based methodcalled Gaussian Process Upper Confidence Bound (GP-UCB). The combination of theISS feedback and the learning algorithms gives a learning-based modularindirect adaptive controller. We show the efficiency of this approach on atwo-link robot manipulator example.
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