In this paper optimal control problems for hyperbolic systems in which different multiple time delays appear in the integral form both in the state equations and in the boundary conditions are considered. Necessary and sufficient conditions of optimality for the Neumann problem are derived. The optimal boundary control is obtained in the feedback form. Making use of the results of Schwartz, the representation of the optimal feedback boundary control is given.
In this paper an optimal distributed control problem for an infinite order hyperbolic system in which different multiple time-varying lags appear both in the state equation and in the boundary condition is considered. Making use of Lion's scheme (Lions 1971), necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functional and constrained control are derived.
