Optimal control via initial conditions of infinite order hyperbolic systems

Various optimization problems associated with the optimal control of second order time delay hyperbolic systems have been studied in [5], [6], [7], [8], [9] and [10] respectively. In this paper, we consider an optimal control problem for a linear infinite order hyperbolic system. The initial conditions are given by control functions. 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 ([12]), necessary and sufficient conditions of optimality for the Dirichlet problem with the quadratic performance functional and constrained control are derived.