Lyapunov stability and adaptive regulation of a class of nonlinear nonautonomous second-order differential equations
type: Item
instance of: scholarly article
title: Lyapunov stability and adaptive regulation of a class of nonlinear nonautonomous second-order differential equations
zbMATH Open document ID: 1020.34042
DOI: 10.1023/A:1015611521852
published in: Nonlinear Dynamics
publication date: 2002-12-15T00:00:00Z
review text: For a class of ordinary nonlinear, nonautonomous second-order differential equations, an adaptive regulation scheme is introduced. The class of equations under consideration contains a number of particular cases with practical applications. Some sufficient Lyapunov stability conditions for the investigated class are presented, which can be used in particular to set an appropriate reference model. The resulting closed-loop adaptive scheme is proved. This scheme involves a parameter estimation scheme of least-square type with all suitable properties in term of estimates, boundedness and asymptotic convergence of estimates to a finite limit as well as time-integrability of the squared adaptation error.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34H05
Mathematics Subject Classification ID: 49J15
zbMATH DE Number: 1845420
zbMATH Keywords: adaptive control
zbMATH Keywords: ordinary nonlinear differential equations
zbMATH Keywords: estimation algorithms
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: boundedness
author: M. De la Sen
reviewed by: Jiří Vaníček
MaRDI profile type: Publication
full work available at URL: a:1015611521852
OpenAlex ID: W2996199228
Wikidata QID: Q57675717
description: scientific article; zbMATH DE number 1845420