Escape Analysis on the Confinement-Escape Problem of a Defender Against an Evader Escaping From a Circular Region

In this paper, we investigate some mathematical properties of the confinement-escape problem of a defender and an evader with respect to a circular region, which was proposed in the author's previous work. Initially, the evader is located inside the circle, the defender patrols on the circle and tries to seal it to prevent the evader' escape; while the evader attempts to escape with avoidance of the defender. Here, we adopt the same control laws of the agents and consider particularly the successful-escape conditions which ensure a monotone-increasing distance (MID) between the defender and the evader as the system evolves, for abbreviation, we call it the escape with the MID to the defender, or simply the MID escape. Then, we: 1) provide some sufficient conditions for the MID escape under different situations; 2) provide the corresponding upper-limit estimations of the escape time; and 3) discuss the characteristics of the analytical results.