Stackelberg strategies for singularly perturbed stochastic systems

Author

Mukaidani, Hiroaki ; Unno, Masaru ; Yamamoto, Takayuki ; Hua Xu ; Dragan, Vasile

Author_Institution

Inst. of Eng., Hiroshima Univ., Higashi-Hiroshima, Japan

fYear

2013

fDate

17-19 July 2013

Firstpage

730

Lastpage

735

Abstract

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.

Keywords

Lyapunov methods; Riccati equations; asymptotic stability; closed loop systems; differential equations; game theory; linear systems; mathematical programming; stochastic systems; CALRE; Ito differential equations; Newton method; SDP; SPSS; asymptotic behavior; cross-coupled algebraic Lyapunov and Riccati equations; linear closed-loop Stackelberg strategy; necessary conditions; semidefinite programming; singularly perturbed stochastic systems; stochastic equations; Convergence; Newton method; Nickel; Riccati equations; Stochastic processes; Stochastic systems;

fLanguage

English

Publisher

ieee

Conference_Titel

Control Conference (ECC), 2013 European

Conference_Location

Zurich

Type

conf

Filename

6669247