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. aanna@mit.edu

3 IBISC CNRS FRE 2873, Université d’Evry, 40 rue du Pelvoux, 91020, Evry Cedex, France said.mammar@iup.univ-evry.fr

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 ...

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