摘要
微分对策是使用微分方程处理双方或多方连续动态冲突、竞争或合作问题的一种数学工具.它已经广泛应用于生物学、经济学、国际关系、计算机科学和军事战略等诸多领域.微分对策实质上是一种双方或多方的最优控制问题,它将现代控制理论与对策论相融合,从而比控制理论具有更强的竞争性、对抗性和适用性.本文根据非线性微分对策理论的控制、均衡及算法阐述了微分对策的理论发展历史,综述了已有结论与算法的本质,总结了现有的研究成果.最后对基于微分对策理论非线性系统的鲁棒性与最优性进行了展望.
Differential game is a mathematical tool for dealing with the problems of continuous dynamic conflict, competition or cooperation with two or more control actions using differential equations. It has been widely employed in biology, economics, international relations, computer science, military strategy and so on. Differential game is essentially an optimal control problem of two or more parties. By integration of modern control theory and game theory, differential game thus has stronger competitiveness, confrontation ability and applicability than control theory. Based on control, equilibrium, and algorithms of nonlinear differential game theory, the paper elaborates on the development history of control, surveys the essence of existing conclusions and algorithms, and summarizes the existing research results. Finally, the perspective of robustness and optimality of nonlinear systems based on differential game are discussed and explored.
出处
《自动化学报》
EI
CSCD
北大核心
2014年第1期1-15,共15页
Acta Automatica Sinica
基金
国家自然科学基金(61073116)
安徽省自然科学基金(1208085MF111)
中国科学院自动化研究所复杂系统管理与控制国家重点实验室开放基金(20120102)
安徽省教育厅自然科学研究项目(KJ2011B123)
安徽省博士后基金
安徽省工业图像处理与分析重点实验室开放基金资助~~
关键词
微分对策
非线性系统
均衡
HJI方程
代价函数
Differential games, nonlinear system, equilibrium, HJI equation, cost function
