追捕逃逸型微分博弈识别域的判别  

Determining the Discriminating Domain for Pursuit-evasion Differential Games

作　　者：韩艳丽[1,2] 高岩[1] 

机构地区：[1]上海理工大学管理学院,上海200093 [2]河南理工大学数信学院,河南焦作454003

出　　处：《信息与控制》2015年第4期411-415,共5页Information and Control

基　　金：国家自然科学基金资助项目(11171221);教育部博士点基金资助项目(20123120110004);上海市高校一流学科(XTKX2012)

摘　　要：针对微分博弈识别域的判别定理很难被具体使用的现象,研究了追捕逃逸型微分博弈关于由不等式表示的光滑区域和非光滑区域的识别域判别问题.利用Gordan引理的等价命题,推导出仿射非线性系统识别域的一种判别条件.这种判别条件类似于优化理论中判别最优性条件的KKT(Karush-Kuhn-Tucker)条件,容易求解.通过举例说明该方法的有效性.最终又将此结果推广到一般非线性系统识别域的判别条件.To address the phenomenon whereby the discriminating theorem of the discriminating domain of differen- tial games is difficult to implement, we study the discriminating domain for pursuit-evasion differential games in a region defined by inequality constraints as being either smooth or unsmooth. Using the equivalence theo- rem of the Gordan Lemma, we obtain the discriminating domain in a manner similar to the Karush-Kuhn- Tucker （KKT） condition in the optimization. The discriminating domain is easy to implement. Through an example, we illustrate the effectiveness of the method and generalize the results to nonlinear control systems.

关 键 词：微分博弈 仿射非线性 识别域 非光滑分析 胜利域 

分 类 号：O231.2[理学—运筹学与控制论]