Distributed control of a retarded hyperbolic system

Various optimization problems associated with the optimal control of distributed parameter systems with retarded arguments appearing in the boundary conditions have been studied recently by [wang], [know], [wong], [kow88a], [kow88b], [kow93a], [kow93b], [kow98a], [kow98b], and [kowdud]. In this paper, we consider an optimal distributed control problem for a linear hyperbolic system in which retarded argument appears in the integral form in the Neumann boundary condition. The performance functional has the quadratic form. The time horizon is fixed. Finally, we impose some constraints on the distributed control. Necessary and sufficient conditions of optimality with the quadratic performance functional and constrained control are derived for the Neumann problem.