Control strategies in a planar pursuit evasion game with energy constraints

AbstractIn this paper, a coplanar pursuit evasion game in the atmosphere, opposing a pursuer employing thrust amplitude and angle of attack as control variables, to a maneuvering evader flying with constant velocity, is considered. The aerodynamic forces acting on the pursuer are explicitly modelled as functions of the angle of attack. The pursuer and evader strategies in the boundary of the capture set are determined for the case of a circular target set. Singular arcs, both for the pursuer and evader, are shown to exist. Along a singular arc, the pursuer moves along a straight line with a thrust amplitude equal to drag, in order to maintain a constant velocity. This constant pursuer velocity is a function of the propulsion system exhaust velocity and the pursuit geometry, and it is shown to be always less than twice the evader's velocity. The pursuit ends with a coasting arc for the pursuer