Optimal control via initial conditions of infinite order hyperbolic systems with the Neumann boundary conditions

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 Neumann boundary conditions are presented. The performance functional has the quadratic form. The time horizon μ 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 Neumann problem with the quadratic performance functional and constrained control are derived.