Fourier spectral methods for numerical solving the problem of boundary control of the linear wave equation

In this paper, a Fourier spectral method is used to reduce the optimal boundary control problem for a two-dimensional wave equation to a countable number of control problems for a one-dimensional wave equation which are transformed to the optimal control problems with integral constraints using the Laplace transform. The numerical integration and differentiation methods are used to approximate the resulting problems with quadratic programming problems. An illustrative numerical example is presented to indicate the efficiency of the proposed method.