Optimal boundary control of one-dimensional multi-span vibrating systems

A class of optimal control problems of one dimensional coupled vibrating systems with control applied at the coupled points is considered. A maximum principle is developed for a class of such optimal problems governed by N linear hyperbolic partial differential equations of second order in time and fourth order in space with variable coefficients. The maximum principle given involves a Hamiltonian which contains an adjoint variable as well as an admissible boundary control function. The proof of the maximum principle is given with the help of convexity arguments. The uniqueness theory of the solution of the optimal control problem is given using convexity arguments.