Abstract
The algebraic regulator and filter Riccati equations of weakly coupled discrete-time stochastic linear control systems are completely and exactly decomposed into reduced-order continuous-time algebraic Riccati equations corresponding to the subsystems. That is, the exact solution of the global discrete algebraic Riccati equation is found in terms of the reduced-order subsystem nonsymmetric continuous-time algebraic Riccati equations. In addition, the optimal global Kaiman filter is decomposed into local optimal filters both driven by the system measurements and the system optimal control inputs. As a result, the optimal linear-quadratic Gaussian control problem for weakly coupled linear discrete systems takes decomposition and parallelism between subsystem filters and controllers.
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