Near optimal linear quadratic regulator for a class of stochastic systems modeled by singularly perturbed itô differential equations with state and control multiplicative white noise

Abstract

In this paper, an optimization problem described by a controlled system modeled by singularly perturbed Itô differential equations having the diffusion part of the fast equation is considered. The main goal of this paper is to deduce the asymptotic structure when the small parameters tend to some constant values. It is shown that the dominant part of this solution consists of a solution of the parameter-independent system of coupled Riccati type equations. In the sequel, a class of parameter-independent approximate controller based on the asymptotic behavior of the ARE is designed. Moreover, the degradation of the cost performance based on the new strategy is established. © 2012 ICIC International.