Preliminary Evaluation and Comparison of Atmospheric Turbulence Rejection Performance for Infinite and Receding Horizon Control in Adaptive Optics Systems

Model-based optimal control such as Linear Quadratic Gaussian (LQG) control has been attracting considerable attention for adaptive optics systems. The ability of LQG to handle the complex dynamics of deformable mirrors and its relatively simple implementation makes LQG attractive for large adaptive optics systems. However, LQG has its own share of drawbacks, such as suboptimal handling of constraints on actuators movements and possible numerical problems in case of fast sampling rate discretisation of the corresponding matrices. Unlike LQG, the Receding Horizon Control (RHC) technique provides control signals for a deformable mirror that are optimal within the prescribed constraints. This is achieved by reformulating the control problem as an online optimisation problem that is solved at each sampling instance. In the unconstrained case, RHC produces the same control signals as LQG. However, when the control signals reach the constraints of actuator's allowable movement in a deformable mirror, RHC finds the control signals that are optimal within those constraints, rather than just clipping the unconstrained optimum as commonly done in LQG control. The article discusses the consequences of high-gain LQG control operation in the case when the constraints on the actuator's movement are reached. It is shown that clipping / saturating the control signals is not only suboptimal, but may be hazardous for the surface of a deformable mirror. The results of numerical simulations indicate that high-gain LQG control can lead to abrupt changes and spikes in the control signal when saturation occurs. The article further discusses a possible link between high-gain LQG and the waffle mode in the closed-loop operation of astronomical adaptive optics systems. Performance evaluation of Receding Horizon Control in terms of atmospheric disturbance rejection and a comparison with Linear Quadratic Gaussian control are performed. The results of the numerical simulations suggest that the disturbance rejection performance in the unconstrained case is the same for LQG and RHC, while RHC clearly outperforms the saturated LQG control in terms of atmospheric turbulence rejection. More importantly, RHC can be used in high-gain mode, unlike LQG, providing better atmospheric disturbance rejection in the constrained case.