Near-Optimal Guidance Law for Ballistic Missile Interception

Aperturbationprocedure is applied to theproblemof Ž ndingan optimalcontrol for a ballisticmissile interceptor. Certain forces, such as thrust and gravity, are assumed to dominate the equations of motion. The optimal control problem is integrable if the remaining forces are neglected; the approximate effects of the neglected forces can be calculated noniteratively and added to the solution. For certain trajectories, however, the aerodynamic forces are not negligible. Including the aerodynamicsdirectly in the dominantdynamicsdestroys the analyticalsolutionupon which the procedure depends. Instead, approximations of the aerodynamic forces are included through narrow pulse functions.This technique produces a good approximationto the optimal control and is computationallymore efŽ cient than previousmethods. Provisions also are made to account for the interceptor’s coast phase and terminal constraints. The near-optimal guidance law is used to produce intercept trajectories against a number of target trajectories. The approximate trajectories compare well with numerically generated optimal trajectories.