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

TL;DR

This paper introduces a modular adaptive control framework for nonlinear systems with uncertainties, combining robust ISS control with model-free learning algorithms like MES and GP-UCB, demonstrated on a robot manipulator.

Contribution

It proposes a novel modular approach integrating ISS control with learning algorithms for adaptive nonlinear system control, enhancing robustness and estimation accuracy.

Findings

Effective uncertainty estimation with MES and GP-UCB

Improved trajectory tracking performance

Validated on a two-link robot manipulator

Abstract

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, where we first design a robust nonlinear state feedback which renders the closed loop input-to-state stable (ISS), where 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 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 show the efficiency of this approach on a two-link robot manipulator example.