Ph.D.Thesis: Online Constrained Receding Horizon Control for Astronomical Adaptive Optics

Ph.D. Thesis

Online Constrained Receding Horizon Control for Astronomical Adaptive Optics

School of Electrical Engineering and Computer Science, the University of Newcastle, Australia. December 2013.

[PDF, mirror, mirror2, Newcastle University repository]


Actuators are naturally limited in the force they can apply, and efficiency often dictates operation that is close to the limits of the permissible values. This is especially true for adaptive optics systems that compensate for the atmospheric turbulence using the mirrors deformable on-the-fly by the actuators. On the one hand, the actuator should use all the authority to bend the deformable mirror and thus compensate the turbulence. On the other hand, the actuators must not damage the mirror by pushing the surface too hard, and the controller must account for these constraints.

This thesis focuses on the high-speed constrained control of deformable mirrors in astronomical adaptive optics. The main approach considered in this work is constrained Receding Horizon Control with Quadratic Programming. A thorough study of the structure and the physics of the control problem allowed exploiting the structure of the problem and an inherently fast sampling rate to hot-start the online optimisation. These features are of crucial importance, making it possible to accelerate the constrained control compared to standard algorithms.

The original contribution of this thesis is a thorough feasibility analysis of the online optimisation algorithms for constrained control in adaptive optics systems. While the Convex Optimisation and the Receding Horizon Control are well studied areas, their application for astronomical adaptive optics has not been systematically studied. The thesis provides the results of numerical simulations that conclusively prove the feasibility of online constrained control of a deformable mirror. Using state-of-the-art Quadratic Optimisation algorithms of my own implementation, a control rate of 10 kHz for a relatively large deformable mirror has been achieved.

The significance of the results of this thesis is a comprehensive performance analysis of various optimisation approaches for constrained optimal control of deformable mirrors in adaptive optics. This is an important step towards attaining the ultimate compensation potential of adaptive optics systems.