Computing optimal boundary controls of a plate by the boundary element method

In recent development of adaptive optics, the problem of shape control of a reflecting mirror is studied. Assume that the mirror is modelled by a thin elastostatic plate. At certain interior points of the plate a number of sensors are located which measure the deformation at those points. We wish to apply boundary controls to the plate so that the sensory data are as close to the prescribed values as possible. In this paper we present a boundary element method to approximate optimal boundary controls for a quadratic cost problem. The method has been tested to have high accuracy and efficiency. Numerical results are also presented.