A Data-Driven ${\cal H}_{2}$-Optimal Control Approach for Adaptive Optics

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Adaptive optics (AO) is used in ground-based astronomical telescopes to improve the resolution by counteracting the effects of atmospheric turbulence. Most AO systems are based on a simple control law that neglects the temporal evolution of the distortions introduced by the atmosphere. This paper presents a data-driven control design approach that is able to exploit the spatio-temporal correlation in the wavefront, without assuming any form of decoupling. The approach consists of a dedicated subspace-identification algorithm to identify an atmospheric disturbance model from open-loop wavefront sensor data, followed by <formula formulatype="inline"><tex>${\cal H}_{2}$</tex></formula>-optimal control design. It is shown that in the case that the deformable mirror and wavefront sensor dynamics can be represented by a delay and a two taps impulse response, it is possible to derive an analytical expression for the <formula formulatype="inline"><tex>${\cal H}_{2}$</tex></formula>-optimal controller. Numerical simulations on AO test bench data demonstrate a performance improvement with respect to the common AO control approach. </para>