Near-optimum regulators for stochastic linear singularly perturbed systems

This paper presents a new approach to approximating linear-quadratic-Gaussian estimation and control problems for singularly perturbed systems. A near-optimal control law, in which separate slow-mode and fast-mode filters are used to estimate the slow and fast variables, is employed to approximate the optimal control law. The order of approximation of the optimal performance is 0(??N) where N is determined by appropriately choosing the coefficients of the near-optimal control law.