Optimal control techniques for the adaptive optics system of the LBT

In this paper we will discuss the application of different optimal control techniques for the adaptive optics system of the LBT telescope which comprises a pyramid wavefront sensor and an adaptive secondary mirror. We have studied the application of both the Kalman and the H∞ filter to estimate the temporal evolution of the phase perturbations due to the atmospheric turbulence and the telescope vibrations. We have evaluated the performance of these control techniques with numerical simulations in preparation of the laboratory tests that will be carried out in the Arcetri laboratories.