一类关于二阶微分方程的追逐微分博弈问题

On Pursuit Differential Game Problems for a Second-order Differential Equations

考虑一类用二阶微分方程描述的多人追逐一人逃逸的追逐微分博弈。在此博弈中,对参与者的控制函数强加上了积分约束,支付函数是博弈结束时追逐者和逃逸者之间距离的下确界。主要目的是建立可容许的追逐策略来保证博弈从任何给定的初始位置是追逐完备的。

In this paper,we consider a pursuit differential game of many pursuers and one evader in Hilbert space,which is described by the second-order differential equations. In process of the game,control functions of the players are subjected to integral constraints,the payoff function is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The main result of this paper is to constructing the admissible strategies of the pursuers to guarantee the completion of pursuit from any given initial position in the game.