Pursuit of a moving target with bounded speed on a directed acyclic graph under partial information

Abstract

Abstract The optimal control of a ‘blind’ airborne pursuer searching for an evader moving on a road network with positive bounded speed toward a set of goal vertices is considered. To aid the pursuer and provide feedback information, certain roads in the network have been instrumented with unattended ground sensors (UGSs) that detect evader motion. When the pursuer arrives at an instrumented node, the UGS therein informs the pursuer if and when the evader visited the node. The pursuer is aware of the bounds on the evader’s speed. Moreover, the embedded graph with the UGSs as vertices and connecting roads as edges is restricted to be a directed acyclic graph (DAG). At time $0$, the evader’s entry into the road network is registered at UGS $1$, the entry node. The pursuer also arrives at the entry node after some delay $d>0$ and is thus informed about the presence of the intruder/evader in the network, whereupon the chase is on. Capture entails the pursuer and evader being co-located at an UGS location. However, if the evader reaches an exit node of the graph without being captured, it is deemed to have escaped. We compute the maximum initial delay $d$ and the ensuing pursuit policy, for which capture is guaranteed.