关键词: 追逃微分博弈, 边界防御, 最优策略, 几何方法

Abstract:

Border security has always been a topic sparking intense debate. Moreover, border morphology realities separating countries are quite complex, exacerbating the complexity of border defence issues. As per relevant literature reviews, there is no perfect universal solution to address border defence problems, which makes it a matter of utmost concern. This paper aims to transform the problem into a pursuit-evasion differential game problem by delineating the border defence scenario. The method of differential game is subsequently used to solve the optimal strategy of the players, which ultimately yields a feasible algorithm. Specifically, this paper uses simple motion to describe player movement in the game, utilises the general equation form of the quadratic curve to demarcate the shape of the boundary, and defines the payoff function as the distance from the capture point to the boundary. The problem is studied by the geometric method, and a more concise value function form is yielded in the case of a circular boundary. The optimal strategy of the player in the game is ultimately constructed. A general algorithm for the quadratic curve boundary is further obtained based on the circular boundary. The model is then stretched from the game of degree to the game of kind, from two dimensions to three dimensions, from M-pursuers against a single evader to M-pursuers against N-evaders, and the result and algorithm are validated by using a numerical simulation.

Key words: pursuit-evasion differential game, border defense, optimal strategy, geometric method