Subsystem-level optimal control of weakly coupled linear stochastic systems composed of N subsystems

In this paper we introduce a transformation for the exact closed-loop decomposition of the optimal control and Kalman filtering tasks of linear weakly coupled stochastic systems composed of N subsystems. In addition to having obtained N completely independent reduce-order subsystem Kalman filters working in parallel, we have obtained the exact solution of the algebraic regulator and filter Riccati equations in terms of the solutions of the corresponding reduced-order subsystem algebraic Riccati equations. The introduced transformation produces a lot of savings especially for on-line computations since it allows parallel processing of information with lower-order-dimensional Kalman filters. The methodology presented is applied to a 17th-order cold-rolling mill.