Construction of Barrier in a Fishing Game With Point Capture
研究一种称为“钓鱼博弈”的追逃问题，其中较快的逃跑者试图穿过两个追捕者之间的空隙，通过将博弈分解为两个子博弈来构建屏障，并求解最优控制策略及获胜时间上界。
This paper addresses a particular pursuit-evasion game, called as "fishing game" where a faster evader attempts to pass the gap between two pursuers. We are concerned with the conditions under which the evader or pursuers can win the game. This is a game of kind in which an essential aspect, barrier, separates the state space into disjoint parts associated with each player's winning region. We present a method of explicit policy to construct the barrier. This method divides the fishing game into two subgames related to the included angle and the relative distances between the evader and the pursuers, respectively, and then analyzes the possibility of capture or escape for each subgame to ascertain the analytical forms of the barrier. Furthermore, we fuse the games of kind and degree by solving the optimal control strategies in the minimum time for each player when the initial state lies in their winning regions. Along with the optimal strategies, the trajectories of the players are delineated and the upper bounds of their winning times are also derived.