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Approximating the Riccati Equation solution for optimal estimation in large-scale Adaptive Optics systems

Adaptive Optics (AO) is a technique that allows the compensation of the atmospheric turbulence effects on ground-based telescopes by means of an actively controlled deformable mirror (DMs), fed back based on the measurements obtained with one or more wavefront sensors (WFSs). For extremely large telescope (more than 20 m in diameter) the number of input and output channels can be in the range of the thousands or tens of thousands, making it problematic to apply optimal control solutions due to the heavy computational load. In this paper we show how it is possible to obtain a quick approximation of the solution of the Discrete Algebraic Riccati Equation (DARE) associated to a certain class of AO optimal control problems, and how the performance are affected by the use of such approximations.