Specific-optimal control with a dual minimal-order observer-based compensator

The steady-state optimal control of a linear time-invariant stochastic system by means of a minimal-order dual-observer-based compensator is considered in this paper. The structure of the compensator is fixed while the associated gains are to be chosen so as to minimize a quadratic penalty on the plant state. Necessary and sufficient conditions for optimality are given, and an explicit solution is displayed. Salient features pertaining to the optimal system are: a decoupling property, a projection property, and an innovation property. Finally, it is shown that this design corresponds to a singular LQG problem, which is precisely the dual of another singular LQG problem: namely Newmann's problem. A complete picture is then given showing clearly the correspondence between the two designs.