Feasibility of Constrained Receding Horizon Control Implementation in Adaptive Optics

Adaptive optics (AO) provide 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 paper presents a feasibility study for receding horizon control (RHC) with online constrained quadratic programming (QP). The results of numerical simulations provided in this paper are based on realistic models obtained from an optical test-bench. We compare QP algorithms that represent three main methods for convex optimization: 1) interior point; 2) active set (AS); and 3) gradient-based algorithms. It is shown that constrained RHC is computationally feasible for moderate-size AO systems using hot-started structure-exploiting AS 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.