This paper considers a target-defense problem of one defender and one adversary (or called intruder), in which the defender tries to approach a desired interception-position between the intruder and the target to intercept the intruder and expel it from the target. The defender adopts this interception and expelling strategy since the defender is assumed to not capture or destroy the intruder. An expelling-decay exponent is introduced to characterize the expelling-decay rate on the intruder. The system is nonlinear, with distinct physical meaning and rich kinematics. The main concern in this paper is the analysis of the kinematic properties. First, two motion patterns of the system are characterized with respect to different values of the system parameters. Then, the stability and the transition condition of the two motion patterns are provided. Finally, the optimal interception of the defender is provided, which interestingly coincides with the transition condition for the two motion patterns. The interpretations for the physical meaning of the optimal interception are also provided.

中文翻译：

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具有拦截和驱逐策略的目标防御问题的运动学特征


本文考虑一个防御者和一个对手（或称为入侵者）的目标防御问题，其中防御者试图接近入侵者和目标之间的期望拦截位置以拦截入侵者并将其驱逐出目标。防御者采取这种拦截和驱逐策略是因为假设防御者不会捕获或摧毁入侵者。引入驱逐衰减指数来表征入侵者的驱逐衰减率。该系统是非线性的，具有鲜明的物理意义和丰富的运动学特征。本文主要关注的是运动学特性的分析。首先，根据系统参数的不同值来表征系统的两种运动模式。然后，给出了两种运动模式的稳定性和过渡条件。最后，提供了防守者的最佳拦截，有趣的是，这与两种运动模式的转换条件一致。还提供了最佳拦截的物理意义的解释。