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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.

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

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