| Abstract: | This paper is concerned with the numerical solution of control problems which consist of minimizing certain quadratic functionals depending on control functions in L 20,1] for some given time T > 0 and bounded with respect to the maximum norm. These control functions act upon the boundary conditions of a vibrating system in one space-dimension which is governed by a wave equation of spatial order 2n They are to be chosen in such a way that a given initial state of vibration at time zero is transferred into the state of rest. This requirement can be expressed by an infinite system of moment equations to be satisfied by the control functions The control problem is approximated by replacing this infinite system by finitely many, say N, equations (truncation) and by choosing piecewise constant functions as controls (discretization). The resulting problem is a quadratic optimization problem which is solved very efficiently by a multiplier method Convergence of the solutions of the approximating problems to the solution of the control problem, as N tends to infinity and the discretization is infinitely refined, is shown under mild assumptions. Numerical results are presented for a vibrating beam |
