Optimal and on-board near-optimal midcourse guidance

Abstract

Optimal midcourse guidance is examined for an air-to-air missile featuring boost-coast-sustain propulsion. A vertical plane, point-mass model is studied with load factor as a control variable. Time-range-energy optimal trajectories are computed, open-loop, via the usual necessary conditions and a multiple-shooting algorithm. A requirement on terminal velocity magnitude is examined for its effect on firing range. Next, a study of the optimal midcourse guidance problem with reduced-order models is presented. The models under study, in addition to the point-mass model, are:

Singularly perturbed model with y as fast variable;

Point mass model with approximation of the induced-drag;

Energy model.

One of the major results in this study is that the reduced-order models are not accurate enough to approximate the optimal trajectories and so are of limited use as reference trajectories in an on-board scheme. Thus, optimal trajectories, computed by using the point-mass model, are selected as the reference trajectories for a closed-loop guidance scheme. Finally, an approach to on-board real-time calculations for an optimal guidance approximation is derived. Extremal fields and neighboring extremal theory ideas are used together with pre-calculated Euler solutions to construct a closed-loop guidance algorithm. The method is applied to the midcourse guidance of an air-to-air missile and was found to perform quite well.