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Optimal Control Problems for Elliptic Systems with Control Constraints and Infinite Number of Variables

G. M. Bahaa, Fatemah El-Shatery

Abstract


In this paper, we consider an optimal control problem for a linear second order elliptic system governed by a self-adjoint elliptic operator with an infinite number of variables. One from the initial conditions is given by control function. Suficient conditions for the existence of a unique solution of such elliptic equations are presented. The performance functional has the quadratic form. Finally, we impose some constraints on the control. Making use of the Lions scheme [18], necessary and su±cient conditions of optimality for the Dirichlet and Neumann problems with the quadratic performance functional and constrained control are derived.

Keywords


Elliptic systems - Dirichlet and Neumann conditions - Existence and uniqueness of solutions - Operators of second order with an infinite number of variables - Optimal control problems.

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