Feedback Control on Nash Equilibrium for Discrete-Time Stochastic Systems with Markovian Jumps: Finite-Horizon Case

被引：3

作者：

Sun, Huiying ^{[1
]}

Jiang, Liuyang ^{[1
]}

Zhang, Weihai ^{[1
]}

机构：

[1] Shandong Univ Sci & Technol, Coll Informat & Elect Engn, Key Lab Robot & Intelligent Technol Shandong Prov, Qingdao 266510, Shandong, Peoples R China

来源：

INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS | 2012年 / 10卷 / 05期

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

Discrete-time stochastic systems; feedback control; generalized difference Riccati equations; linear quadratic differential games; Markovian jumps; nonzero-sum; MULTIPLICATIVE NOISE;

D O I：

10.1007/s12555-012-0510-6

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we consider the feedback control on nonzero-sum linear quadratic (LQ) differential games in finite horizon for discrete-time stochastic systems with Markovian jump parameters and multiplicative noise. Four-coupled generalized difference Riccati equations (GDREs) are obtained, which are essential to find the optimal Nash equilibrium strategies and the optimal cost values of the LQ differential games. Furthermore, an iterative algorithm is given to solve the four-coupled GDREs. Finally, a suboptimal solution of the LQ differential games is proposed based on a convex optimization approach and a simplification of the suboptimal solution is given. Simulation examples are presented to illustrate the effectiveness of the iterative algorithm and the suboptimal solution.

引用

页码：940 / 946

页数：7

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