Control-Theoretic Models of Environmental Crime

TL;DR

This paper develops two control-theoretic models to analyze how environmental criminals plan resource extraction under surveillance, considering different patrol strategies and detection probabilities, with applications to complex protected areas.

Contribution

It introduces novel optimal control and dynamic programming models for perpetrators' decision-making under surveillance, incorporating realistic patrol and terrain complexities.

Findings

Models effectively simulate criminal path-planning under various patrol strategies.

Numerical methods handle complex geometries and non-uniform detection rates.

Results inform better surveillance strategies for environmental protection.

Abstract

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 multi-objective dynamic programming. Our efficient numerical methods are illustrated on several examples with complicated geometry and terrain of protected areas, non-uniform distribution of protected resources, and spatially non-uniform detection rates due to aerial or ground patrols.