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Necessary conditions for constrained distributed parameter systems with deviating argument

Published online by Cambridge University Press:  17 February 2009

Mohammad A. Kazemi
Mohammad A. Kazemi
Affiliation:
Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina28223.
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Abstract

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In this paper we consider an optimal control problem governed by a system of nonlinear hyperbolic partial differential equations with deviating argument, Darboux-type boundary conditions and terminal state inequality constraints. The control variables are assumed to be measurable and the state variables are assumed to belong to a Sobolev space. We derive an integral representation of the increments of the functionals involved, and using separation theorems of functional analysis, obtain necessary conditions for optimality in the form of a Pontryagin maximum principle. The approach presented here applies equally well to other nonlinear constrained distributed parameters with deviating argument.

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 4 , April 1996 , pp. 495 - 511
Copyright
Copyright © Australian Mathematical Society 1996

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