The goal of this project is to control Adaptive Optics (AO) systems. Features of the AO systems will be modeled in the usual control framework to allow existing control analysis, design and adaptation methodologies to be applied. New methodologies will be developed as needed. This research will examine the use of previously developed Linear-Quadratic-Gaussian (LQG) designs in both open loop and closed loop adaptive control architectures. The research will also determine the important modeling uncertainties of AO systems and apply or develop robust stability and performance analyses to AO systems. Finally, the research will extend LQG based designs and robustness analyses to Multi-Conjugate Adaptive Optics (MCAO) systems. This research will use data from the Max-Planck Instiut fur Astronomie (MPIA) telescope at Calar Alto, Spain, and simulations developed for the European Southern Observatory (ESO)