离散双线性系统鞍点均衡的迭代算法

广东工业大学学报 ›› 2010, Vol. 27 ›› Issue (1): 8-11.

离散双线性系统鞍点均衡的迭代算法

广东工业大学1. 管理学院; 2. 经济与贸易学院, 广东广州510520

出版日期:2010-03-25 发布日期:2010-03-25
作者简介:朱怀念( 1985-), 男, 硕士研究生, 主要研究方向为管理系统工程、博弈论.
基金资助:
国家自然科学基金资助项目( 70771029) ; 广东省自然科学基金资助项目( 070117); 内蒙古自治区高等学校科学技术项目( NJ09137); 广东工业大学青年基金资助项目( 082050)

Iterative A lgorithm for Saddle-point Equilibrium ofDiscrete-time Bilinear Systems

1. Schoo l o fM anagem ent; 2. School o f Econom ics and Comm erce, Guangdong University of Technology, Guangzhou 510520, China

Online:2010-03-25 Published:2010-03-25

摘要/Abstract

摘要： 针对有限时间段内的离散时不变双线性系统二次型性能指标的鞍点均衡问题, 通过应用动态规划原理, 将鞍点均衡问题转化为双线性系统的非线性两点边值问题, 再引入一个变换, 将非线性两点边值问题转化成一个具有"分离"形式的"线性"两点边值问题, 最后利用一种新的迭代算法对"线性"两点边值问题进行求解, 为离散双线性
系统的微分博弈理论求解提供了一种新的思路.

关键词: 离散双线性系统; 鞍点均衡; R icca ti方程

Abstract: Regarding the saddle-po int equ ilibrium for discrete t ime bilinear-quadratic controlin the f in ite t ime, the sadd le-po int equ ilibrium is converted into a non linear tw o po int boundary va lue by using the dynam ic prog ramm ing pr incipa.l Then by using a transfo rmation, the nonlinear tw o po int boundary value is transfo rmed in to a "linear" two point boundary va luew ith "separate" form. Finally, a new iterative a lgorithm is constructed to solve the problem, w hich provides a new approach to the problem w ith the differential gam es o f discrete-time b ilinear systems.

Key words: discrete-t ime bilinear system; sadd le-po int equilibrium; R iccat i equation

朱怀念1, 张成科2, 武赛1, 宾宁1. 离散双线性系统鞍点均衡的迭代算法[J]. 广东工业大学学报, 2010, 27(1): 8-11.

ZHU Huai-Nian1, ZHANG Cheng-Ke2, WU Sai1, BIN Ning1. Iterative A lgorithm for Saddle-point Equilibrium ofDiscrete-time Bilinear Systems[J]. Journal of Guangdong University of Technology, 2010, 27(1): 8-11.

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