Global adaptive stabilization of cascade nonlinear systems
type: Item
instance of: scholarly article
title: Global adaptive stabilization of cascade nonlinear systems
zbMATH Open document ID: 0876.93082
DOI: 10.1016/S0005-1098(96)00181-1
author: Mrdjan Jankovic
author: P. V. Kokotović
author: Rodolphe Sepulchre
published in: Automatica
publication date: 1997-07-03T00:00:00Z
review text: The paper deals with global adaptive stabilization for systems of the form \[ \begin{aligned} \dot x & = Fx+ H(\xi)x+ h^T(\xi)\theta+ g^T(x,\xi,y)y,\\ \dot\xi & = A\xi+ b^T(x,\xi,y)\theta y,\\ \dot y & = \varphi^T(x,\xi,y)\theta+ u\end{aligned} \] with \(H(0)= 0\), \(h(0)=0\); \(\theta\in\mathbb{R}^p\) is the vector of the unknown parameters. The authors use a Lyapunov function for the zero dynamics with respect to \(y\) and obtain adaptive stabilization by using a modified Lyapunov function of the form \[ V_\theta(x,\xi,y,\widetilde\theta)= W_\theta(x,\xi)+ \textstyle{{1\over 2}} y^2+ \textstyle{{1\over 2}} |\widetilde\theta|^2, \] where \(\widetilde\theta\) is the estimation error for the parameter \(\theta\) and \(W\) is the Lyapunov function associated to the stable zero dynamics with respect to \(y\).
Mathematics Subject Classification ID: 93D21
Mathematics Subject Classification ID: 93A99
Mathematics Subject Classification ID: 93C10
zbMATH DE Number: 1008768
zbMATH Keywords: global adaptive stabilization
zbMATH Keywords: Lyapunov function
reviewed by: Vladimir Răsvan
MaRDI profile type: Publication
cites work: Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems
cites work: Constructive Lyapunov stabilization of nonlinear cascade systems
cites work: Systematic design of adaptive controllers for feedback linearizable systems
cites work: Q4273828
cites work: A positive real condition for global stabilization of nonlinear systems
cites work: Adaptive nonlinear control without overparametrization
cites work: Adaptive nonlinear design with controller-identifier separation and swapping
cites work: Remarks on smooth feedback stabilization of nonlinear systems
cites work: Global asymptotic stabilization of general nonlinear systems with stable free dynamics via passivity and bounded feedback
cites work: Adding integrations, saturated controls, and stabilization for feedforward systems
cites work: Nonlinear adaptive control of feedback passive systems
cites work: Q5284153
full work available at URL: s0005-1098(96)00181-1
OpenAlex ID: W1993375989
description: scientific article; zbMATH DE number 1008768