On application of constrained receding horizon control in astronomical adaptive optics

Abstract

Control system design for adaptive optics is becoming more complex and sophisticated with increasing demands on the compensation of atmospheric turbulence. Contemporary controllers used in adaptive optics systems are optimised in the sense of a cost function (linear quadratic regulators) or to a worst case scenario (robust H_∞ controllers). Prediction, to some extent, can be incorporated into the controllers using the Kalman filter and a model of the atmospheric turbulence. Despite the growing number of publications on adaptive optics control systems, only the unconstrained case is usually considered. Accounting for the physical constraints of the adaptive optics system components, such as limited actuator stroke, still represents a problem. As a possible solution, one can consider constrained receding horizon control (RHC), also known as Model Predictive Control (MPC). The ability of RHC to handle constraints and make predictions of the future control signals makes it attractive for application in astronomical adaptive optics. The main potential difficulty with the application of RHC is its heavy computational load. This paper presents preliminary results on numerical simulations of an adaptive optics system controlled by constrained RHC. In particular, the case of output disturbance rejection is considered. The results of numerical simulations are provided. Finally, methods for improving the computational performance of constrained receding horizon controllers in adaptive optics are also discussed.