On existence problems for the optimal control of certain nonlinear integral equations of Urysohn type
type: Item
instance of: scholarly article
title: On existence problems for the optimal control of certain nonlinear integral equations of Urysohn type
zbMATH Open document ID: 0534.49008
DOI: 10.1007/BF00935326
published in: Journal of Optimization Theory and Applications
publication date: 1984-01-01T00:00:00Z
review text: In the papers of \textit{T. Zolezzi} [Ann. Mat. pura appl. IV. Ser. 91, 97- 118 (1972; Zbl 0238.49003)], \textit{T. S. Angell} [J. Optimization Theory Appl. 19, 29-45 (1976; Zbl 0305.49021)] and \textit{M. L. Bennati} [Ann. Mat. Pura Appl., IV. Ser. 121, 187-197 (1979; Zbl 0422.49013)] existence results have been obtained for optimal control problems whose state equations are described by certain nonlinear integral equations of Urysohn type. We generalize and synthesize these results by formulating a general lower closure result from which the results in the above mentioned papers are shown to follow. In the course of this, we also present a novel and rather abstract treatment of existence problems for variable-time optimal control, quite in the spirit of a previous paper of the author [SIAM J. Control Optimization 20, 198-210 (1982; Zbl 0499.49006)].
Mathematics Subject Classification ID: 49J99
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 54C08
Mathematics Subject Classification ID: 28A20
zbMATH DE Number: 3848092
zbMATH Keywords: nonlinear integral equations of Urysohn type
zbMATH Keywords: variable-time optimal control
author: Erik J. Balder
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3848092