SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1441-1466, January 2020.
We present two models of perpetrators' decision-making in extracting resources from a protected area. It is assumed that the authorities conduct surveillance to counter the extraction activities, and that perpetrators choose their post-extraction paths to balance the time/hardship of travel against the expected losses from a possible detection. In our first model, the authorities are assumed to use ground patrols and the protected resources are confiscated as soon as the extractor is observed with them. The perpetrators' path-planning is modeled using the optimal control of randomly terminated process. In our second model, the authorities use aerial patrols, with the apprehension of perpetrators and confiscation of resources delayed until their exit from the protected area. In this case the path-planning is based on multiobjective dynamic programming. Our efficient numerical methods are illustrated through several examples with complicated geometry and terrain of protected areas, nonuniform distribution of protected resources, and spatially nonuniform detection rates due to aerial or ground patrols.

中文翻译：

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环境犯罪的控制理论模型

SIAM应用数学杂志，第80卷，第3期，第1441-1466页，2020年1月。
在从保护区中提取资源时，我们提供了两种犯罪者的决策模型。假定当局进行监视以对抗提取活动，并且犯罪者选择其提取后的路径，以平衡行进的时间/艰辛与可能发现的预期损失。在我们的第一个模型中，假定当局使用地面巡逻，并且一旦观察到采掘者，就会没收受保护的资源。使用对随机终止过程的最佳控制，对犯罪者的路径规划进行建模。在我们的第二种模式中，当局使用空中巡逻，逮捕肇事者和没收资源被推迟到他们离开保护区之前。在这种情况下，路径规划是基于多目标动态规划的。通过几个示例来说明我们的有效数值方法，这些示例包括受保护区域的复杂几何形状和地形，受保护资源的分布不均匀以及由于空中或地面巡逻而造成的空间不均匀检测率。