Stackelberg Strategies for Singularly Perturbed Stochastic Systems

In this paper, a linear closed-loop Stackelberg strategy for a class of singularly perturbed stochastic systems (SPSS) governed by Ito differential equations is considered. Necessary conditions for the solution are established via a set of cross-coupled algebraic Lyapunov and Riccati equations (CALREs). After studying the asymptotic behavior of the solution for these stochastic equations, two new numerical algorithms based on Newton's method and semidefinite programming (SDP) for solving CALREs are given. A numerical example is solved to demonstrate the efficiency of the proposed algorithm.