ON A PURSUIT PROBLEM FORn-PERSON LINEAR DIFFERENTIAL AND DISCRETE GAMES WITH INTEGRAL CONSTRAINTS

Abstract

We propose a single panel liquid crystal (LC) device that is switchable between reflective and transmissive modes. Operation in the reflective mode can be achieved by applying a vertical field to a dye-doped LC device, whereas the device can be in-plane switched for operation in the transmissive mode. Image inversion that was inevitable in a single panel device using a reflective polarizer is effectively eliminated through the absorption of ambient light by the dye-doped LCs. We believe that the proposed device can be applied to various display systems for outdoor mobile use.

Evasion differential game of two evaders and one pursuer with integral constraints

“…This is because we can pass a two-dimensional plane through the initial positions 0 1 0 2 0 , , x y y of the players in n n , and then consider evasion from the projection x of the pursuer on this plane. According to the theorem, the evaders moving on the plane can avoid to coincide with the projection of the pursuer x , i. , then pursuit can be completed (see, for example, [8], [13]). The results of the paper can be developed towards the evasion differential game with many evaders.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14]. More specifically, there were a few works on the related problem in the case of many pursuers and one evader.…”

“…Satimov et al [13] studied a linear pursuit differential game of such case with integral constraints on controls of players in n n . The game was described by the following equations:…”

An Approach for Solving Discrete Game Problems with Total Constraints on Controls

“…A large number of works are devoted to differential games where the position of the players changes continuously in time (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). Zero-sum differential games were first considered in the book of Isaacs [5] who derived the main equation of the theory of differential games.…”

“…There are a few papers that study discrete games under total constraints (see, e.g., [14][15][16][19][20][21][22]).…”