线性微分博弈系统的识别域判别

Determining discriminating domain for linear differential games

针对一般非线性系统识别域的判别定理难以被具体应用这一现象,利用非光滑分析理论,研究线性微分博弈系统的一个有界识别域问题,即如果一个闭集是识别域,则此集合的凸包也是识别域,从而得到一个多面体识别域.提出了该问题的一种有效算法,该算法简便易行,利用转换定理即可得到系统的胜利域.最后通过算例验证了所提出算法的可行性和有效性.

Aimming at the phenomenon that the discriminating theorem of discriminating domain of the general nonlinear system is difficult to be used, a bounded discriminating domain for linear pursuit-evasion differential games is studied. If a closed set is a discriminating domain of the differential games, the convex hull of the set is also a discriminating domain of the differential games. A polyhedral discriminating domain is obtained, and an efficient algorithm is given, which is easy to be used. By using the alternative theorem, the victory domain of the differential games can be obtained. An example is given to show the feasibility and effectiveness of the proposed algorithm.