Capturability of 3D RTPN guidance law against true-arbitrarily maneuvering target with maneuverability limitation

The capturability of the Three-Dimensional (3D) Realistic True Proportional Navigation (RTPN) guidance law is thoroughly analyzed. The true-arbitrarily maneuvering target is considered, which maneuvers along an arbitrary direction in 3D space with an arbitrary but upper-bounded acceleration. The whole nonlinear relative kinematics between the interceptor and target is taken into account. First, the upper-bound of commanded acceleration of 3D RTPN is deduced, using a novel Lyapunov-like approach. Second, the reasonable selection range of navigation gain of 3D RTPN is analyzed, when the maneuver limitation of interceptor is considered. After that, a more realistic definition of capture is adopted, i.e., the relative range is smaller than an acceptable miss-distance while the approaching speed is larger than a required impact speed. Unlike previous researches which present Two-Dimensional (2D) capture regions, the inequality analysis technique is utilized to obtain the 3D capture region, where the three coordinates are the closing speed, transversal relative speed, and relative range. The obtained capture region could be taken as a sufficient-but-unnecessary condition of capture. The new theoretical findings are all given in explicit expressions and are more general than previous results.