Chattering variational limits of control systems †

Chattering variational limits of control systems † Abstract. Variational convergence is developed for optimal control problems depending on time-varying parameters. Systems with chattering parameters serve then s variational limits when the parameters are rapidly oscillating. Continuity of the value, robustness of controls and continuous dependence of optimal controls are examined. 1991 Mathematics Subject Classification: 49J45, 49N99. 1. Introduction This paper addresses the variational convergence problem of optimal control Systems. The form we choose to work with is a minimization problem with constraint equation depending on a time-varying parameter. The variational convergence of this parameter function is sought. Namely, we consider a family of control Systems minimize J Q (x, u, t, (f)) dt (VQ) -£=f(x,u,t,Q(ty)dt x( ) = x0. Each element in the family is determined by a parameter function = (·). We seek a convergence notion for the collection of parameter functions such that: (i) the cost functional with a fixed control depends continuously on , and (ii) the value of vary continuously with . Research supported by a grant from the Basic Research Fund, The Israel Academy of Science and Humanities. * Incumbent of the Hettie H. Heineman Professorial Chair in Mathematics. Zvi Artstein With these two properties, the following approximation scheine applies http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

Chattering variational limits of control systems †

Forum Mathematicum, Volume 5 (5) – Jan 1, 1993

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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1993.5.369
Publisher site
See Article on Publisher Site

Abstract

Abstract. Variational convergence is developed for optimal control problems depending on time-varying parameters. Systems with chattering parameters serve then s variational limits when the parameters are rapidly oscillating. Continuity of the value, robustness of controls and continuous dependence of optimal controls are examined. 1991 Mathematics Subject Classification: 49J45, 49N99. 1. Introduction This paper addresses the variational convergence problem of optimal control Systems. The form we choose to work with is a minimization problem with constraint equation depending on a time-varying parameter. The variational convergence of this parameter function is sought. Namely, we consider a family of control Systems minimize J Q (x, u, t, (f)) dt (VQ) -£=f(x,u,t,Q(ty)dt x( ) = x0. Each element in the family is determined by a parameter function = (·). We seek a convergence notion for the collection of parameter functions such that: (i) the cost functional with a fixed control depends continuously on , and (ii) the value of vary continuously with . Research supported by a grant from the Basic Research Fund, The Israel Academy of Science and Humanities. * Incumbent of the Hettie H. Heineman Professorial Chair in Mathematics. Zvi Artstein With these two properties, the following approximation scheine applies

Journal

Forum Mathematicumde Gruyter

Published: Jan 1, 1993

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