Adaptive control of nonlinear dynamical systems using a model reference approach
type: Item
instance of: scholarly article
title: Adaptive control of nonlinear dynamical systems using a model reference approach
zbMATH Open document ID: 1056.93041
DOI: 10.1023/A:1022854621106
author: David J. Wagg
published in: Meccanica
publication date: 2003-12-09T00:00:00Z
review text: The paper contains a review of linear model reference adaptive control designed by hyperstability and Lyapunov techniques. The system reads \[ \dot{x}_{e}=A_mx_e + B\Phi^Tw-d(t),\quad \Phi=k_e-k, \] \[ k(t)=C_1y_ew+C_2\int_{t_0}^{t}y_e(\tau)w(\tau)\,d\tau \] and \(y_e=Cx_e\); the coefficients \(C_1\) and \(C_2\) are to be chosen in order to obtain a stable system. The same kind of problem is reviewed for a nonlinear system \[ \dot{x}=f_1(x,t) + g_1(u,t),\qquad \dot{x}_m =F_2(x,t) + g_2(r(t),t), \] where the second equation means the reference model description. This case is solved by feedback linearization and by applying afterwards the previous approach. An application of chaotic motion control is given.
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93B18
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 2014994
zbMATH Keywords: Lyapunov function
zbMATH Keywords: chaos control
zbMATH Keywords: model reference adaptive control
zbMATH Keywords: hyperstability
zbMATH Keywords: feedback linearization
reviewed by: Vladimir Răsvan
MaRDI profile type: Publication
full work available at URL: a:1022854621106
OpenAlex ID: W1542278835
Wikidata QID: Q61941988
description: scientific article; zbMATH DE number 2014994