奇异双线性系统二次型微分博弈的鞍点均衡

运筹学学报 ›› 2011, Vol. 15 ›› Issue (2): 45-52.

奇异双线性系统二次型微分博弈的鞍点均衡

朱怀念, 张成科, 宾宁

出版日期:2011-06-15 发布日期:2011-06-15

Saddle-Point Equilibrium of Quadratic Differential Game for Singular Bilinear Systems

ZHU Huai-Nian, ZHANG Cheng-Ke, BIN Ning

Online:2011-06-15 Published:2011-06-15
Supported by:
Supported by the National Natural Science Fund of China (070098, 70801019), the Natural Science Fund of Guangdong Province (070117, 04009475), and the Natural Science Fund of Inner Mongolia Autonomous Region (2010MS1007).

摘要/Abstract

摘要： 研究了有限时间段内的奇异双线性二次型性能指标的鞍点均衡问题. 针对问题求解的复杂性，引入降阶变换将问题分解为快、慢两个子系统，然后利用极大值原理求得了系统的最优控制策略.最后给出了数值算例的仿真以验证算法的正确性和有效性.

关键词: 奇异双线性系统, 微分博弈, 鞍点均衡

Abstract: This paper investigates the saddle-point equilibrium of quadratic differential game for singular bilinear systems in the finite time. As it is complex to solve the problem, a reduced-order transformation is introduced in order to obtain the fast and slow subsystems, then, the optimal control is obtained by using the maximum principle. In the end, the simulation of a numerical example is presented to illustrate the correctness and effectiveness of the proposed algorithm.

Key words: singular bilinear system, differential game, saddle-point equilibrium

中图分类号:

朱怀念, 张成科, 宾宁. 奇异双线性系统二次型微分博弈的鞍点均衡[J]. 运筹学学报, 2011, 15(2): 45-52.

ZHU Huai-Nian, ZHANG Cheng-Ke, BIN Ning. Saddle-Point Equilibrium of Quadratic Differential Game for Singular Bilinear Systems[J]. Operations Research Transactions, 2011, 15(2): 45-52.

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