Optimal control problem for infinite order hyperbolic system with mixed control-state constraints

A distributed control problem for a hyperbolic system with mixed control-state constraints involving operator of infinite order is considered. The performance index is more general than the quadratic one and has an integral form. Making use of the Dubovitskii-Mityutin theorem, the optimality conditions for the Neumann problem are derived. Yet the problem considered here is more general than the problems in El-Zahaby [proceedings of the International conference on mathematics (Trends and Developments) of the Egyptian Mathematical Society, Cairo, Egypt, 28-31 December 2002, and Submitted for Publication in J Egyptian Math soc], Gali and El-Saify [proceedings of the International conference on functional-differential systems and related topics, vol III, Poland, 1983, pp 99-103] and Gali et al.