The Continuous Classical Optimal Control of a Coupled of Nonlinear Elliptic Equations

Abstract

This paper is concern with the existence and the uniqueness solution of the state vector of a couple of nonlinear elliptic partial differential equations for a given continuous classical control vector. Also the existence theorem of a continuous classical optimal control vector governing by the considered couple of nonlinear partial differential equation of elliptic type with equality and inequality constraints is developed and proved. The existence and the uniqueness solution of the couple of adjoint equations associated with the considered couple equations of the state is studded. The derivation of the Frcéhet derivative of the Hamiltonian is obtained. The necessary conditions theorem so as the sufficient conditions theorem of optimality of the constrained problem are developed and proved.

Keywords: Classical optimal control, system of nonlinear elliptic, necessary and sufficient conditions.