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 Itô 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.