Optimal synthesis in certain terminal control problems : PMM vol. 42, no. 6, 1978, pp. 989–999

A class of problems of terminal control of multi-dimensional systems reducible to one-dimensional is investigated. Similar problems of time-optimal response for autonomous and nonautonomous systems were considered, for instance, in [1]. The solution derived here is based on sufficient conditions of the dynamic programming method [2]. Ways are developed for the derivation of an analytic solution of the problem of synthesis and, also, for the determination of optimal-phase trajectory and of programmed control. Problems of energy-optimal consumption for stabilizing the rotations of a dynamically symmetric solid body using a limited power motive system are solved [3].