Optimal control law for adaptive optics on extremely large telescopes

The traditional control law used on adaptive optics for a 10-m class telescope or smaller is an integrator control law in which the integrator gain is chosen in order to minimize the error propagation mode by mode. It has been shown that this kind of control law is sub-optimal and a Kalman/LQG control has been proposed to optimally control 10-m class AO systems. This control law is hard to apply on a system designed for a larger telescope. Typically, the next generation telescopes size will be between 30 and 42 meters. Such a so-called Extremely Large Telescope does not allow to use computing demanding control laws. We analyze the limitations of Kalman/LQG control law when the number of degrees of freedom increases and we propose an alternative, based on the ensemble Kalman filtering. We study the efficiency of such a control law applied to the Adaptive Optics control and compare it to traditional Kalman /LQG.