In this paper, some hyperbolic systems involving infinite order operator defined on W have been considered. Distributed control for  coupled systems with Dirichlet conditions has been established. The existence and uniqueness for the state of these systems have been proved. Then the necessary and sufficient conditions for optimality of the control with some constraints have been obtained by a set of equations and inequalities.

coupled hyperbolic systems, optimal control, infinite order, distributed control problem, control constraints, Dirichlet conditions.