Solution of Fuller’s problem on the basis of the joint Pontryagin-Hamilton-Ostrogradskii principle

摘要

The present study is devoted to the synthesis of the optimal control of a dynamic system. It is proved that application of the method of needle variation to the invariant features of effective motion is a promising approach to increasing the efficiency with which problems involved in the synthesis of optimal control are solved. The Hamilton-Ostrogradskii action integral, to which the Pontryagin needle variation is applied, is adopted as such a feature in the study. As a result, a minium condition for the objective functional is obtained; this condition is termed the joint maximum principle.