Nonlinear adaptive control of feedback passive systems
type: Item
instance of: scholarly article
title: Nonlinear adaptive control of feedback passive systems
zbMATH Open document ID: 0833.93033
DOI: 10.1016/0005-1098(95)00004-G
published in: Automatica
publication date: 1996-03-11T00:00:00Z
review text: The authors apply to Yakubovich theory coming from the early 1970's, the concept of nonlinear adaptive control. Let the plant equations be: \(\dot x= F(x,u, \xi, v)\), \(y= H(x,u, \xi,v)\). Here \(x\), \(u\), \(y\) denote state, input and output vectors, \(\xi\) is the vector of parameters, \(v\) is an external disturbance. The control objective is given by: \(Q_t\leq 0\), \(t\geq t_n\). The authors wish to find a two-level algorithm such that the system meets its objective, while the trajectories belong to prescribed sets. The first level belongs to the main loop of the controlled system, and is called the control law. The second level forms the adaptation loop, and is called the adaptation law. The following cases are discussed separately: 1) Memoryless objective functional \(Q_t= Q(x, v)+ \overline {Q}\); 2) Integral objective functional; 3) Feedback passive system; 4) Adaptive feedback passivity. Theorems giving sufficient conditions for passivity and strict passivity of the output are proved. An example of a forced Lienard equation illustrates behavior of the output which depends on some choice for the parameters.
reviewed by: Vadim Komkov
Mathematics Subject Classification ID: 93C40
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93D10
zbMATH DE Number: 806691
zbMATH Keywords: speed-gradient technique
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: nonlinear adaptive control
zbMATH Keywords: passivity
author: María M. Seron
author: David J. Hill
author: Alexander Fradkov
MaRDI profile type: Publication
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Wikidata QID: Q127089112
description: scientific article; zbMATH DE number 806691