Matrix selection of saddles for pursuit/evasion differential games

The uncertainty of terminate time in pursuit/evasion differential games (DG) makes it difficult to solve using usual numerical solution methods, what is more seriousness, the first order necessary condition can not be obtained in some pursuit/evasion DG. Matrix selection of saddles is proposed to solve this problem. This selection method is similar to the cooperative coevolution in genetic algorithms, it proceeds from the saddles of DG directly, transferring the pursuit of different goals for cost function to the selection of elements in matrix which is maximum in its column and simultaneously is minimum in its row, furthermore genetic algorithms are used to obtain the saddles of DG. The matrix selection method is verified by a practical pursuit/evasion DG.