This paper studies a two-person linear-quadratic-Gaussian pursuit-evasion differential game with costly but controlled information. One player can decide when to observe the other player's state. However, one observation of another player's state comes with two costs: the direct cost of observing and the implicit cost of exposing his state. We call games of this type a Pursuit-Evasion-Exposure-Concealment (PEEC) game. The PEEC game constitutes two types of strategies: The control strategies and the observation strategies. We fully characterize the Nash control strategies of the PEEC game using techniques such as completing squares and the calculus of variations. We show that the derivation of the Nash observation strategies and the Nash control strategies can be decoupled. We develop a set of necessary conditions that facilitate the numerical computation of the Nash observation strategies. We show, in theory, that players with less maneuverability prefer concealment to exposure. We also show that when the game's horizon goes to infinity, the Nash observation strategy is to observe periodically, and the expected distance between the pursuer and the evader goes to zero with a bounded second moment. We conducted a series of numerical experiments to study the proposed PEEC game. We illustrate the numerical results using both figures and animation. Numerical results show that the pursuer can maintain high-grade performance even when the number of observations is limited. We also show that an evader with low maneuverability can still escape if the evader increases his stealthiness.
翻译:本文用昂贵但受控的信息来研究双人线性线性赤道- 加利- 加利- 加利- 逃避追逐差异的游戏。 一个玩家可以决定何时观察另一个玩家的状态。 但是, 一个观察另一个玩家的状态需要两种成本: 观察的直接成本和暴露他的国家的隐含成本。 我们称之为“ 追逐- Evasion- 探索- 隐蔽” (PEEC) 游戏。 PEEC 游戏由两种策略组成: 控制策略和观察策略。 我们充分描述PEEC 游戏的纳什控制策略, 使用诸如完成正方和变异计算等技术。 我们显示, 纳什观察战略和纳什控制策略的衍生可以分解两种成本: 观测策略的直接成本和纳什控制策略的衍生成本可以分解两种成本。 我们开发了一套必要的条件, 方便对纳什观察策略进行数字的计算。 我们从理论上看, 较不易操作的玩家更倾向于隐藏的游戏。 我们还表明, 当游戏的视野到不精确, 纳什观察策略可以定期观察, 以及预期的递离级观察和逃避的观察和隐藏的游戏的距离之间的距离之间的距离, 我们的观察方法可以显示。 我们用数字显示, 显示, 显示, 我们的游戏的游戏的游戏的游戏的游戏的数值显示, 显示, 显示, 和预判变变速性实验显示, 我们的数值显示, 显示, 显示, 显示, 显示, 显示, 数字性试验的 数字性 显示, 显示, 显示, 显示, 显示, 我们的 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 我们的 显示, 我们的 数字性 数字 显示, 显示, 显示, 我们的 显示, 显示, 显示, 显示, 显示, 显示, 我们的 显示, 数字的 数字的 显示, 数字的 数字的 数字的 显示, 显示, 我们的 数字 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示, 显示,