Optimal control of systems governed by partial differential equations with integral inequality constraints

Kazemi-Dehkordi, M. A.

doi:10.1016/0362-546x(84)90052-x

Nonlinear Analysis: Theory, Methods & Applications

1984

DOI: 10.1016/0362-546x(84)90052-x

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Optimal control of systems governed by partial differential equations with integral inequality constraints

M. A. Kazemi-Dehkordi

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1995

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Cited by 4 publications

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A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

Kazemi

1995

J. Aust. Math. Soc. Series B, Appl. Math

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In this paper a class of optimal control problems with distributed parameters is considered. The governing equations are nonlinear first order partial differential equations that arise in the study of heterogeneous reactors and control of chemical processes. The main focus of the present paper is the mathematical theory underlying the algorithm. A conditional gradient method is used to devise an algorithm for solving such optimal control problems. A formula for the Frgchet derivative of the objective function is obtained, and its properties are studied. A necessary condition for optimality in terms of the Fr6chet derivative is presented, and then it is shown that any accumulation point of the sequence of admissible controls generated by the algorithm satisfies this necessary condition for optimality.

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A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

Kazemi

1995

J. Aust. Math. Soc. Series B, Appl. Math

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Necessary conditions for constrained distributed parameter systems with deviating argument

Kazemi

1996

J. Aust. Math. Soc. Series B, Appl. Math

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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.

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Tarkiainen

Tuomala

1999

Computational Economics

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Optimal control of systems governed by partial differential equations with integral inequality constraints

Cited by 4 publications

References 5 publications

A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

A gradient technique for an optimal control problem governed by a system of nonlinear first order partial differential equations

Necessary conditions for constrained distributed parameter systems with deviating argument

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