Adaptive optics application of distributed control design for decomposable systems

This article concerns a class of linear systems which we call ¿decomposable systems¿. Such systems can be thought of as the interconnection of a number of identical subsystems, and they can be used to model certain classes of large scale systems. In this paper we will show how the results for control design of this class of systems can be applied in the field of adaptive optics, specifically to the problem of controlling the deformation of a mirror under the effect of cross-coupled actuator. We will show that the technique allows the design of a distributed H₂ controller for a mirror of any size, with a computational cost that does not increase with the size of the mirror.