Pursuit-evasion

Suppose there is a single evader and the task is to determine where it might be. In this case, $l_i = 0, u_i = 1$ for each shadow at $t = t_0$ . There are three possibilities for each shadow at $t = t_f$ : 1) $l_i = u_i = 0$ (the evader is not in $s_i$ ), 2) $l_i = u_i = 1$ (the evader is definitely in $s_i$ ), and 3) $l_i = 0, u_i = 1$ (the evader may or may not be in $s_i$ ). Note that this is a passive version of the pursuit-evasion problem. We do not determine a trajectory that is guaranteed to detect the evader. In general, this problem is NP-hard [12]. Nevertheless, the calculation method proposed in this paper can be used with heuristic search techniques (or even human operators) to correctly maintain the status of the pursuit.