Geodesic
$H_\infty$ control design for an adaptive optics system
Kybernetika, Tome 35 (1999) no. 1, pp. 69-81 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper we first present a full order $H_\infty $ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_\infty $ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_\infty $ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_\infty $ controller it is found that the dynamical behavior of the reduced order $H_\infty $ controller can be accurately approximated by a single-input, single-output (SISO) transfer function (TF) multiplied by the inverse of the adaptive optics plant dc gain. This observation then leads to a general design methodology which only requires the synthesis of a SISO $H_\infty $ controller and multiplication by constant matrices.
In this paper we first present a full order $H_\infty $ controller for a multi- input, multi-output (MIMO) adaptive optics system. We apply model reduction techniques to the full order $H_\infty $ controller and demonstrate that the closed-loop (CL) system with the reduced order $H_\infty $ controller achieves the same high level of performance. Upon closer examination of the structure of the reduced order $H_\infty $ controller it is found that the dynamical behavior of the reduced order $H_\infty $ controller can be accurately approximated by a single-input, single-output (SISO) transfer function (TF) multiplied by the inverse of the adaptive optics plant dc gain. This observation then leads to a general design methodology which only requires the synthesis of a SISO $H_\infty $ controller and multiplication by constant matrices.
Classification : 93B11, 93B15, 93B36, 93C95
Keywords: multi-input; multi-output; adaptive optics system; model reduction techniques; $H_\infty$ control 
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     title = {$H_\infty$ control design for an adaptive optics system},
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Denis, Nikolaos; Looze, Douglas; Huang, Jim; Castañon, David. $H_\infty$ control design for an adaptive optics system. Kybernetika, Tome 35 (1999) no. 1, pp. 69-81. http://geodesic.mathdoc.fr/item/KYB_1999_35_1_a6/

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