Segmented mirrors are to be used in the next generation of the ground-based optical telescopes to increase the size of the primary mirrors. A larger primary mirror enables the collection of more light, which results in higher image resolutions. The main reason behind the choice of segmented mirrors over monolithic mirrors is to reduce manufacturing, transportation, and maintenance costs of the overall system. However, segmented mirrors bring new challenges to the telescope design and control problem. The large number of inputs and outputs make the computations for centralized control schemes intractable. Centralized controllers also result in systems that are vulnerable to a complete system failure due to a malfunction of the controller.

Distributed control is a viable alternative that requires the use of a network of simple individual segment controllers that can address two levels of coupling among segments and achieve the same performance objectives. Since segments share a common support structure, there exists a coupling among segments at the dynamics level. Any control action in one segment may excite the natural modes of the support structure and disturb other segments through this common support. In addition, the objective of maintaining a smooth mirror surface requires minimization of the relative displacements among neighbouring segment edges. This creates another level of coupling generally referred to as the objective coupling.

This dissertation investigates the distributed H_∞ control of the segmented next generation telescope primary mirrors in the presence of wind disturbances. Three distributed H_∞ control techniques are proposed and tested on three segmented primary mirror models:​ the dynamically uncoupled model, the dynamically coupled model and the finite element model of Thirty Meter Telescope (TMT) project. It is shown that the distributed H_∞ controllers are able to satisfy the stringent imaging performance requirements.