Feasibility of constrained receding horizon control implementation in adaptive optics

Adaptive optics (AO) provides real-time compensation for atmospheric turbulence to improve the resolution of images acquired by ground-based optical telescopes. The actuators in deformable mirrors, which are used as correctors, are constrained by a maximal allowable movement. The control techniques used in current AO systems do not account for these constraints, leading to inferior performance and a risk of damage of the deformable mirror's surface. This article presents a feasibility study for Receding Horizon Control (RHC) with on-line constrained Quadratic Programming (QP). The results of numerical simulations provided in this article are based on realistic models obtained from an optical test-bench. We compare QP algorithms that represent three main methods for convex optimisation: Interior Point, Active Set, and Gradient-based algorithms. It is shown that constrained RHC is computationally feasible for moderate-size adaptive optics systems using hot-started structure-exploiting Active Set QP solvers with bound constraints. An evaluation of performance indicates that RHC is advantageous in terms of atmospheric turbulence rejection in the case of active constraints.