Aircraft Missile Avoidance

The game of two cars defined by Rufus Isaacs is visualized here in terms of missile avoidance by an aircraft. With the system dynamics specified and confined to the horizontal plane, the distinctiveness between Isaacs' original problem and ours lies not only in the choice of parameters, but in the choice of assigned player rationale as well. In particular, we obtain three different capture zones. The capture zones are defined in terms of the barriers separating regions of capture from noncapture. We obtain a game barrier by assuming both the missile and the aircraft use optimal (qualitative game) control, a proportional navigation barrier by assuming the missile is using proportional navigation and the aircraft is using optimal evasive control, and a green barrier by assuming no control action by the aircraft with the missile using optimal pursuing control. The first two barriers allow for a qualitative comparison of proportional navigation guidance-to-guidance based on game theory. The green barrier gives important information when no maneuver is required to avoid the missile.