Optimal guidance of proportional navigation

In the optimal guidance laws of proportional navigation, most problems are formulated to obtain the optimal magnitude of applied commanded acceleration under pure or true proportional navigation. Now in this paper, the optimal direction of applied commanded acceleration is derived under conventional proportional navigation with maneuvering or nonmanenvering targets, in which the line-of-sight deflection angle and the energy expenditure until intercept are minimized. Some related important characteristics, such as capture criterion and energy expenditure, are investigated and discussed in detail. Also, some typical examples of target maneuver are introduced. Target maneuver will decrease the capture area and increase the energy cost for effective intercept of target.