H2-optimal control of an adaptive optics system

Abstract

The problem of finding the closed-loop optimal controller is formulated in an H2-optimal control framework. This provides a natural way to account for the fact that in many AO systems the wavefront phase cannot be measured directly. Given a multi-variable disturbance model of both wavefront slopes and wavefront phases,3 this provides a general procedure to compute the closed-loop controller. If the wavefront sensor and deformable mirror are static and the only dynamics in the system is a unit-sample delay between measurement and correction, an analytical expression for the optimal controller can be derived. This results in a control approach, in which both identification and computation of the optimal controller are exclusively based on standard matrix operations. No Riccati equation needs to be solved to compute the optimal controller. The proposed H2-control approach is numerically validated on open-loop wavefront sensor data and its performance is compared with the common approach. Also the sensitivity to measurement noise is considered.