Positional strategies in fractional order differential games

Abstract

Problems of the branch of mathematics called differential games, which today find their versatile applications in physics and engineering, are devoted to the construction of chase control when the states of the object are known only at given times in advance. Sufficient conditions for the possibility of completing the pursuit in the sense of hitting a small neighborhood of the terminal set are obtained. A method is indicated for constructing a positional strategy of the pursuer that infers a trajectory to a given neighborhood of the terminal set by the time determined by the first direct method of the theory differential pursuit games. In this case, the chasing party cannot use the fleeing player’s control to build its control; therefore, according to the condition of the problem, the chaser builds its control if it knows the state of the object at the given times in advance.

Solutions to the problem of differential games with electric oscillations by finite difference methods

“…We partially use the methods seen in [4][5][6][7][8] and their analogies. And adjoins the works [9][10][11][12][13][14][15][16][17][18][19][20]. First, we reduce the problem posed to a finite difference game, and then we pass to a discrete game.…”