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Optimal Control for n X n Coupled Parabolic Systems with Control-Constrained and Infinite Number of Variables

G. M. Bahaa, Fatemah El-Shatery


The main goal of this paper, by using the theorems of Lions, J.L. et al.[21, 22], is to study a distributed control problem for n x n coupled systems of parabolic type with an infinite number of variables. Yet the problem considered there is more general than the one in [1-8,10,11,13,20]. The controls are allowed to be in the space n. The necessary and sufficient conditions for optimality of the control are obtained and the set of inequalities that defining the optimal control of these systems are also obtained. Several mathematical examples for derived optimality conditions are presented.


Optimal control problems, Dirichlet conditions, Existence and uniqueness of solutions, n£n coupled systems of parabolic type, Operators with an infinite number of variables.

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