Optimal control of causal differential-algebraic systems
type: Item
instance of: scholarly article
title: Optimal control of causal differential-algebraic systems
zbMATH Open document ID: 1020.49001
DOI: 10.1016/S0022-247X(02)00040-9
author: Tomáş Roubíçek
author: Michael Valášek
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-09-08T00:00:00Z
review text: The paper deals with optimal control of systems whose dynamics are of the type \(\dot{x} = f (t,x,y,u)\), \(g(t,x,y,u)=0\), where \(u\) is the control, \(x\) and \(y\) are, respectively, the ``slow'' and the ``fast'' components of the state. One system of this type has index \(k\) if one needs to differentiate the algebraic constraint, \(g(t,x,y,u)=0\), \((k-1)\) times in order to obtain the underlying system of ODE's. The authors present regularity conditions that allow the given optimal control problem to be reduced to an equivalent problem with dynamics of the type \(\dot{x} = f (t,x,u)\) by using an implicit function argument. This reduction is used to obtain sufficient conditions for the existence of optimal controls and necessary optimality conditions under the form of suitable versions of the maximum principle. This is done separately for systems of index 1, 2 and 3. Beyond index 3 the method becomes impractical for general cases because of the complexity of the conditions involved. An application to an index-3 problem arising in robotics is presented.
Mathematics Subject Classification ID: 49J15
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 70E60
Mathematics Subject Classification ID: 93C85
zbMATH DE Number: 1797501
zbMATH Keywords: optimal control
zbMATH Keywords: differential-algebraic equations
zbMATH Keywords: existence theory
zbMATH Keywords: maximum principle
zbMATH Keywords: necessary optimality conditions
zbMATH Keywords: robotics
reviewed by: Manuel Guerra
MaRDI profile type: Publication
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full work available at URL: s0022-247x(02)00040-9
OpenAlex ID: W2059850999
description: scientific article; zbMATH DE number 1797501