Infinite horizon linear quadratic differential games for discrete-time stochastic systems

This paper deals with the infinite horizon linear quadratic （LQ） differential games for discrete-time stochas- tic systems with both state and control dependent noise. The Popov-Belevitch-Hautus （PBH） criteria for exact observability and exact detectability of discrete-time stochastic systems are pr...

Full description

Saved in:
Bibliographic Details
Published inJournal of control theory and applications Vol. 10; no. 3; pp. 391 - 396
Main Authors Sun, Huiying, Jiang, Liuyang, Zhang, Weihai
Format Journal Article
LanguageEnglish
Published Heidelberg South China University of Technology and Academy of Mathematics and Systems Science, CAS 01.08.2012
Subjects
Brief Papers
Complexity
Computational Intelligence
Control
Control and Systems Theory
Differential games
Engineering
Horizon
Linear quadratic
Mathematical analysis
Mechatronics
Optimization
Robotics
Stochastic systems
Stochasticity
Strategy
Systems Theory
地平线
时域
离散时间
精确能观性
线性二次型
随机微分对策
随机微分方程
随机系统
Nash equilibrium
Discrete-time stochastic systems
Exact observability
Differential games
Exact detectability
Online AccessGet full text

Cover

More Information
Summary:This paper deals with the infinite horizon linear quadratic （LQ） differential games for discrete-time stochas- tic systems with both state and control dependent noise. The Popov-Belevitch-Hautus （PBH） criteria for exact observability and exact detectability of discrete-time stochastic systems are presented. By means of them, we give the optimal strategies （Nash equilibrium strategies） and the optimal cost values for infinite horizon stochastic differential games. It indicates that the infinite horizon LQ stochastic differential gaines are associated with four coupled matrix-valued equations. Further- more, an iterative algorithm is proposed to solve the four coupled equations. Finally, an example is given to demonstrate our results.
Bibliography:Discrete-time stochastic systems; Exact observability; Exact detectability; Differential games; Nash equi-librium
This paper deals with the infinite horizon linear quadratic （LQ） differential games for discrete-time stochas- tic systems with both state and control dependent noise. The Popov-Belevitch-Hautus （PBH） criteria for exact observability and exact detectability of discrete-time stochastic systems are presented. By means of them, we give the optimal strategies （Nash equilibrium strategies） and the optimal cost values for infinite horizon stochastic differential games. It indicates that the infinite horizon LQ stochastic differential gaines are associated with four coupled matrix-valued equations. Further- more, an iterative algorithm is proposed to solve the four coupled equations. Finally, an example is given to demonstrate our results.
44-1600/TP
ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1672-6340
1993-0623
DOI:10.1007/s11768-012-1004-z