Hybrid system for target tracking in triangulation graphs

We investigate a variation of the art gallery problem in which a team of mobile guards tries to track an unpredictable intruder in a simply-connected polygonal environment. The guards are deployed based on the strategy initially proposed in [1] which restricts them to move along a specific diagonal within the environment. However, the intruder can move freely within the environment. We define critical regions to generate event-triggered strategies for the guards. Additionally, a hybrid automaton is designed to model the problem, and sufficient conditions are presented for [n/4] guards for persistent surveillance.