Optimal control via initial state of an infinite order hyperbolic system

Various optimization problems associated with the optimal control of second order time delay hyperbolic systems have been studied in and respectively. In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. One from the initial conditions is given by control function. Sufficient conditions for the existence of a unique solution of such hyperbolic equations with the Dirichlet boundary conditions are presented. The performance functional has the quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the control. Making use of the Lions scheme, necessary and sufficient conditions of optimality for the Dirichlet problem with the quadratic performance functional and constrained control are derived.