A variational technique for optimal boundary control in a hyperbolic problem

Abstract

The authors study the problem of controlling the boundary functions in a one dimensional hyperbolic problem by minimizing the functional including the final state. They prove the existence and uniqueness of the solution of the optimal control problem under consideration and give a necessary condition to the optimal solution by a variational inequality via the solution of the adjoint problem. Finally, they prove that a minimizing sequence defined by the method of projection of the gradient converges to the optimal solution.