On the Asymptotic Structure of the Stabilizing Solution of a Class of Singularly Perturbed Riccati Equation of Stochastic Control

摘要

An optimal control problem for a system of linear It?o differential equations with two fast time scales and Markovian jumping is considered. The asymptotic structure for the stabilizing solution satisfying a sign condition for the coupled stochastic algebraic Riccati equations is derived. Furthermore, a near optimal control whose gain matrices do not depend upon small parameters is discussed.