Extremum Seeking-based Indirect Adaptive Control and Feedback Gains Auto-Tuning for Nonlinear Systems

We present in this chapter some recent results on learning-based adaptive control for nonlinear systems. We first study the problem of adaptive trajectory tracking for nonlinear systems, and show that for the class of nonlinear systems with parametric uncertainties which can be rendered integral Input-to-State stable w.r.t. the parameter estimation error, that it is possible to merge together the integral Input-to-State stabilizing feedback controller and a model-free extremum seeking (ES) algorithm to realize a learning-based adaptive controller. We investigate the performance of this approach in term of tracking errors upper-bounds, for two different ES algorithms. Next, we propose a learning-based approach to auto-tune the feedback gains for nonlinear stabilizing controllers. Book chapter in: Control Theory: Perspectives, Applications and Developments 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., 2015 201 Broadway, Cambridge, Massachusetts 02139 EXTREMUM SEEKING-BASED INDIRECT ADAPTIVE CONTROL AND FEEDBACK GAINS AUTO-TUNING FOR NONLINEAR SYSTEMS Mouhacine Benosman∗ Mitsubishi Electric Research Laboratories Cambridge, USA To appear in Control Theory: Perspectives, Applications and Developments, 2015 Abstract We present in this chapter some recent results on learning-based adaptive control for nonlinear systems. We first study the problem of adaptive trajectory tracking for nonlinear systems. We focus on the class of nonlinear systems with parametric uncertainties, which can be rendered integral Input-to-State Stable (iISS) w.r.t. the parameter estimation error. We argue, for this particular class of systems, that it is possible to merge together the integral Input-to-State stabilizing feedback controller and a model-free extremum seeking (ES) algorithm, to realize a learning-based adaptive controller. We investigate the performance of this approach in term of tracking error upper-bounds, for two different ES algorithms. Next, we consider the class of nonlinear systems affine in the control, and propose a learning-based approach to iteratively auto-tune the feedback gains for nonlinear stabilizing controllers.We present in this chapter some recent results on learning-based adaptive control for nonlinear systems. We first study the problem of adaptive trajectory tracking for nonlinear systems. We focus on the class of nonlinear systems with parametric uncertainties, which can be rendered integral Input-to-State Stable (iISS) w.r.t. the parameter estimation error. We argue, for this particular class of systems, that it is possible to merge together the integral Input-to-State stabilizing feedback controller and a model-free extremum seeking (ES) algorithm, to realize a learning-based adaptive controller. We investigate the performance of this approach in term of tracking error upper-bounds, for two different ES algorithms. Next, we consider the class of nonlinear systems affine in the control, and propose a learning-based approach to iteratively auto-tune the feedback gains for nonlinear stabilizing controllers.