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

ZHU  Huai-Nian; ZHANG  Cheng-Ke; WU  Sai; BIN  Ning

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

更新时间：2026-05-27

- Iterative A lgorithm for Saddle-point Equilibrium ofDiscrete-time Bilinear Systems
- Vol. 27, Issue 1, Pages: 8-11(2010)
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- Online First：25 March 2010，
  
  Published：2010
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朱怀念, 张成科, 武赛, 宾宁. 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-Nian, ZHANG Cheng-Ke, WU Sai, et al. Iterative A lgorithm for Saddle-point Equilibrium ofDiscrete-time Bilinear Systems[J]. 2010, 27(1): 8-11.
朱怀念, 张成科, 武赛, 宾宁. 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. DOI：

ZHU Huai-Nian, ZHANG Cheng-Ke, WU Sai, et al. Iterative A lgorithm for Saddle-point Equilibrium ofDiscrete-time Bilinear Systems[J]. 2010, 27(1): 8-11. DOI：

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.

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.

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references

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K im Y J, K im B S, Lim M T. Composite contro l for s ingu larly perturbed b ilinea r system s v ia successive Ga lerkin approximation[J]. IEE Proc-Contro l Theo ry App,l 2003, 150( 5): 483-488.

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Zhang Chengke, Gao Jingguang, Chen G elin, eta .l Sadd lepoint Equ ilibrium Strategy of the bilinear-quadratic Twoperson Zero- sum Dynam ic Gam e: A Recursive Approach [J]. DCDIS 2005, 3: 1158-1165.

Zhang Cheng Ke, Sunpeihong, Yuan wan l.i The Quadratic Saddlepoint Equilibrium Strategy for Discrete Time Bilinear System [C] / / Inte rnational Conference of Industr ial Engineering and Engineering Management, Zheng zhou, 2008.

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Baser T, OlsderG J.Dynam ic non- coopera tive gam e theory [M]. New York: A cadem ic Press, 1991.

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