Linear Quadratic Guidance Laws for Imposing a Terminal Intercept Angle

Linear quadratic guidance laws that explicitly enable imposing a predetermined intercept angle are presented. Two such guidance laws are derived, using optimal control and differential game theories, for arbitrary-order linear missile dynamics. The obtained guidance laws are dependent on the well-known zero-effort miss distance and on a new variable denoted zero-effort angle. It is shown that imposing the terminal angle constraint raises considerably the gains of the guidance laws. Theoretic conditions for the existence of a saddle-point solution in the differential game are also derived. These conditions show that imposing the terminal angle constraint requires a higher maneuverability advantage from the missile. The performance of the proposed guidance laws is investigated using a nonlinear two-dimensional simulation of the missile's lateral dynamics and relative kinematics, while assuming first-order dynamics for the target's evasive maneuvers. Using a Monte Carlo study, it is shown that, for the investigated problem, a target can be intercepted with a negligible miss distance and intercept angle error even when the target maneuvers and there are large initial heading errors.