A geometric approach to nonlinear singularly perturbed control systems
type: Item
instance of: scholarly article
title: A geometric approach to nonlinear singularly perturbed control systems
zbMATH Open document ID: 0633.93033
DOI: 10.1016/0005-1098(88)90005-2
author: Riccardo Marino
author: P. V. Kokotović
published in: Automatica
publication date: 1988-01-01T00:00:00Z
review text: The paper considers a class of nonlinear control systems depending on a parameter \(dz/dt=Z(z,\epsilon,u)\). A necessary and sufficient condition including ``conservation'', ``equilibrium'' and ``transversality'' properties is presented under which the system can be transformed into a singular perturbation system \(dx/d\tau =\epsilon X(x,y,\epsilon,u)\), \(dy/d\tau =Y(x,y,\epsilon,u)\) such that \(\{\) (x,y), \(Y(x,y,0,u)=0\}\) is a smooth control-dependent manifold of constant dimension. As examples a point-mass model of an aircraft and a model of a manipulator with flexible joints are discussed.
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93B27
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 93C95
zbMATH DE Number: 4031511
zbMATH Keywords: nonlinear control systems
zbMATH Keywords: conservation
zbMATH Keywords: equilibrium
zbMATH Keywords: transversality
zbMATH Keywords: singular perturbation system
zbMATH Keywords: aircraft
zbMATH Keywords: manipulator with flexible joints
reviewed by: A. L. Dontchev
MaRDI profile type: Publication
full work available at URL: 0005-1098(88)90005-2
OpenAlex ID: W1976070636
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description: scientific article; zbMATH DE number 4031511