Optimality conditions for infinite order hyperbolic control problem with non-standard functional and time delay

Abstract

A distributed control problem for the hyperbolic operator with infinite order and time delay is considered. The performance index has an integral form. Constraints on controls are imposed. To obtain optimality conditions for the Neumann problem the generalization of the Dubovitskii-Milyutin Theorem from [35, 36] was applied.

Keywords:

• Optimal control problems
• Neumann problem
• hyperbolic operators with infinite order and time delay
• Dubovitskii-Miyutin theorem
• conical approximations
• optimality conditions
• Weierstrass theorem