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Constrained control of low order adaptive optics systems using a fast suboptimal solution based on “feedback from coupling”

This paper presents a suboptimal control technique based on the approximate constrained inverse of the Hessian matrix. The Hessian matrix is split into its diagonal part (the decoupled problem with a trivial inverse) and the off-diagonal part (the coupled component). Instead of the exact inversion of the Hessian matrix and solution of the Quadratic Programming (QP), an iterative approximate constrained inverse is calculated. The control problem can be therefore viewed as a decentralised control formulation with corrections from coupling - that is, feedback from coupling. The results of numerical simulations for a MIMO coupled system are reported. The MIMO system models a low-order adaptive optics system with a deformable mirror driven by an array of piezoelectric actuators. A comparison of the proposed method against Model Predictive Control with QP solvers is performed.