Solution methods for differential games

Zero-Sum Pursuit-Evasion Differential Games with Many Objects: Survey of Publications

“…Dimension of the phase vector x = (x 1 , x 2 ) is equal to two and the phase vector x is absent in the right-hand part of system (24). So, we have a standard differential game with a fixed termination instant T .…”

“…They arise in subroutines for constructing Minkowski sum and difference, especially, if the sets are non-convex. In the case of convex polygons in the plane, these algorithms can be implemented very effectively and easy [24,31,67]. Computational problems grow catastrophically with increasing dimension of the phase vector of system (19).…”

Extremal aiming in problems with an unknown level of dynamic disturbance

“…Its specific embodiment is associated with the possibility of the analytical or numerical construction of stable bridges. In the theory of differential games, there is a considerable number of publications [11][12][13][14][15][16][17][18][19][20][21] dealing with algorithms for the numerical construction of the most stable bridges and the sets for the level of the value function. The methods which have been developed can be used to construct the above mentioned family of stable bridges.…”

On Level Sets With "Narrow Throats" in Linear Differential Games

“…There are several publications describing other numerical methods for constructing level sets of the value function in linear differential games with fixed terminal time (Ushakov (1981), Subbotin and Patsko (1984), Taras'ev et al (1988), Grigorenko et al (1993), Bardi and Dolcetta (1997), Kurzhanski and Valyi (1997), Cardaliaguet et al (1999), Polovinkin et al (2001)). The examples presented in this paper can be used for testing the accuracy and efficiency of such methods.…”