Necessary Optimality Conditions for Constrained Optimal Control Problems Governed by Parabolic Equations-Reference-Cited by-同舟云学术

Necessary Optimality Conditions for Constrained Optimal Control Problems Governed by Parabolic Equations

Published:2003-08 Issue:8 Volume:9 Page:949-963
ISSN:1077-5463
Container-title:Journal of Vibration and Control
language:en
Short-container-title:Journal of Vibration and Control

Author:

Farag M. H.¹

Affiliation:

1. Mathematics Department, Faculty of Education, Ibri, Sultanate of Oman

Abstract

Abstract: In this paper we deal with the necessary conditions satisfied by the optimal control of a system governed by a quasi-linear parabolic equation. We consider constraints on the state and on the control through the coefficients of this equation. The optimal control problem has been converted to one of the optimization problem using a penalty function technique. We give the existence and uniqueness theorem for the solution of the considered problem. We derive the sufficient differentiability conditions of the cost functional and its gradient formulae based on solving the adjoint system. We establish the necessary conditions for the considered problem, and finally we present a numerical example.

Publisher

SAGE Publications

Subject

Mechanical Engineering,Mechanics of Materials,Aerospace Engineering,Automotive Engineering,General Materials Science

Link

http://journals.sagepub.com/doi/pdf/10.1177/10775463030098003

Reference10 articles.

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3. An existence and uniqueness theorem for one optimal control problem

4. Farag, S. H. and Farag, M. H. 2000a, “Necessary optimality conditions in control problems for hyperbolic equations,” Journal of the Egyptian Mathematical Society 8(2), 189-198 .

5. On an optimal control problem for a quasilinear parabolic equation