Pure proportional navigation against time-varying target maneuvers

Capturability of the pure proportional navigation (PPN) guidance law against a target executing bounded piecewise continuous time-varying maneuvers is investigated A qualitative analysis is carried out to obtain a set of sufficient conditions for capture defined on the engagement parameters and initial conditions. These conditions are significantly less restrictive than the ones obtained previously by others using the Liapunov method. It is shown that the actual capture region for time-varying target maneuvers, obtained by using the conditions derived in this work, is much larger than that obtained from the Liapunov technique. We also show that though a bounded time-varying target maneuver does change the constant target maneuver capture region to some extent, it does not reduce it drastically. Further, we show that the worst case capture region is obtained when the target executes a constant maneuver equal to the bound on the maneuver level. Some bounds on the missile lateral acceleration are also obtained for certain regions in the engagement plane. These results are generalizations and extensions of existing results on the capturability of the PPN guidance law against targets executing constant or time-varying target maneuvers.