Linear-quadratic-Gaussian problem for a new class of singularly perturbed stochastic systems

This paper addresses the numerical solution of the linear-quadratic-Gaussian (LQG) for a new class of singularly perturbed (SP) system using fixed-point recursive algorithms. Traditionally, SP systems have been studied for one vector input controlling both slow and fast subsystems. We show that the LQG problem can be solved efficiently for systems containing two vector inputs governing the slow and fast subsystems independently. The recursive algorithm solution helps avoid numerical stiffness problems that can arise by solving the regulator and/or filter continuous algebraic Riccati equations (CAREs) using established methods. In addition, the solutions given in terms of reduced-order Lyapunov equations and CAREs simplify controller and Kalman filter designs.