In previous studies of optimal proportional navigation, the problem are most formulated to obtain the optimal magnitude of applied commanded acceleration under pure or true proportional navigation. Recently, the optimal direction of applied commanded acceleration is derived and discussed under conventional proportional navigation. Now in this article, the optimal guidance of modified proportional navigation is studied with maneuvering or nonmaneuvering target, in which the energy expenditure till intercept is minimized. From the result of this study, it shows that true proportional navigation is the exact optimal solution for a nonmaneuvering target or near-optimal solution for a maneuvering target. Some related important characteristics, such as capture criterion and energy expenditure, are investigated and discussed in detail. Also, a typical example of target maneuver is introduced to illustrate the effect of target maneuver easily. It shows that the target maneuver will decrease the capture area and increase the energy cost for effective intercept of target.
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