Extremal problems for second order hyperbolic systems involving multiple time delays

Abstract

Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in theNeumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.

Keywords

• optimal control theory
• boundary control
• second order hyperbolic systems
• multiple time delays
• electric long lines