Trajectory optimization for Long-Range Air-Defense Missile with a Constraint on Capability of Error Correction

A method of designing optimal parabolic trajectory for long range air-defense interceptor missile with a constraint on capability of error correction in its terminal guidance phase is proposed. In this method a constraint condition on the error correction capability in finite terminal guidance phase for the missile with bounded acceleration is presented to replace the traditional constraint on instantaneous normal acceleration. A minimum time problem under the constraint is solved using the nonlinear programming optimal control theory. Simulation results for some typical scenarios of long range interception show that the optimal trajectories satisfy a series of constraints including not only the error correction capability, but also the constraint on and maximum angle of attack, and the constraints on terminal flight path angle and terminal velocity.