Taming Heterogeneity and Complexity of Embedded Control

A New Adaptive Controller for Systems with Multilinear Parameterization

 

N-Parameters Case

Mariana Netto¹, —Anuradha Annaswamy², —Saïd Mammar³, — Nicoleta Minoiu¹

¹ LCPC/INRETS - LIVIC Laboratoire sur les Interactions Véhicule-Infrastructure- Conducteur, 14, Route de la Minière, Bât 824, 78000, Versailles, France {netto,minoiu}@lcpc.fr

² Adaptive Control Laboratory, Department of Mechanical Egineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. [e-mail]

³ IBISC CNRS FRE 2873, Université d’Evry, 40 rue du Pelvoux, 91020, Evry Cedex, France [e-mail]

ABSTRACT. Adaptive control of nonlinearly parameterized (NLP) systems is an unknown field, where few results have been proposed up to now. In this paper, we propose a new adaptive control algorithm for systems with multilinear parameterization. Differently from our previous work where the two parameters case was considered, we treat here the general case of n-parameters. It is important to note that the class of multilinear parameterizations belongs to the class of nonlinear parameterizations. The proposed controller is a non certainty equivalence one where only the original parameters, without then the need of overparameterization, are adapted. Simulations show the efficacy of the approach.

KEYWORDS: adaptive control, nonlinear parameterization, convexity, concavity, multilinear parameterization

1. Introduction

Among the systems that have nonlinear parameterizations, we can cite a ...