Near-optimum regulators for stochastic linear singularly perturbed systems

This paper presents a new approach to the decomposition and approximation of linear-quadratic-Gaussian estimation and control problems for singularly perturbed systems. The Kalman filter is decomposed into separate slow-mode and fast-mode filters via the use of a decoupling transformation. A near-optimal control law is derived by approximating the coefficients of the optimal control law. The order of approximation of the optimal performance is where is the order of approximation of the coefficients.