A spatial non-dynamic LQG controller: Part II, theory

For part I see ibid., p.3326-32 (2004). Fundamental theory is derived for control of adaptive optics used in astronomical telescopes, and for possible other applications involving shape control, vibrations, and other spatial control problems in which the control system acts much faster than a fixed process, or the observable and controllable subspaces are both finite dimensional. The theory is developed from a feedforward rather than feedback viewpoint. The LQG separation into estimation followed by deterministic control is shown to hold even under non-dynamic and feedforward formulation. Then observable and controllable subspaces can be defined, which must hold for a fixed process even in the dynamic case. An example of a dynamic process (adaptive optics) is given in which observability and controllability can be used to reduce the state space to finite dimension. Corresponding costs are evaluated, and compared with any linear controller in both feedforward and feedback.