Learning‐based iterative modular adaptive control for nonlinear systems

In this paper we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative 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 propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data-driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a datadriven multi-parametric extremum seeking (MES) method, which guarantees local convergence results, and the second is a Bayesian optimization-based method called Gaussian Process Upper Confidence Bound (GPUCB), which guarantees global results in a compact search set. The combination of the ISS feedback and the data-driven learning algorithms gives a learning-based modular indirect adaptive controller. We show the efficiency of this approach on a two-link robot manipulator numerical example. International Journal of adaptive control and signal processing This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c © Mitsubishi Electric Research Laboratories, Inc., 2018 201 Broadway, Cambridge, Massachusetts 02139 INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING Int. J. Adapt. Control Signal Process. 0000; 00:1–30 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/acs Learning-Based Iterative Modular Adaptive Control for Nonlinear Systems Mouhacine Benosman, Amir-massoud Farahmand, Meng Xia Mitsubishi Electric Research Laboratories, 201 Broadway Street, Cambridge, MA 02139, USA (Email: m benosman@ieee.org),Mathworks, USA.