New methods for optimal control and filtering of singularly perturbed linear discrete stochastic systems

In this paper the algebraic regulator and filter Riccati equations of singularly perturbed discrete-time control systems are completely and exactly decomposed into reduced-order continuous-time algebraic Riccati equations corresponding to the slow and fast time scales. In addition, the optimal global Kalman filter is decomposed into pure-slow and pure-fast local optimal filters both driven by the system measurements and the system optimal control input. It is shown that these two filters can be implemented independently in the different time scales. As a result, the optimal linear-quadratic Gaussian control problem for singularly perturbed linear discrete systems takes the complete decomposition and parallelism between pure-slow and pure-fast filters and controllers.