Direct Method for Resolution of Optimal Control Problem with Free Initial Condition

The theory of control analyzes the proprieties of commanded systems. Problems of optimal control OC have been intensively investigated in the world literature for over forty years. During this period, series of fundamental results have been obtained, among which should be noted the maximum principle Pontryagin et al., 1962 and dynamic programming Bellman, 1963 . For many of the problems of the optimal control theory OCT , adequate solutions are found Bryson and Yu-chi, 1969, Lee and Markus, 1967, Gabasov and Kirillova, 1977, 1978, 1980 . Results of the theory were taken up in various fields of science, engineering, and economics. The present paper aims at extending the constructive methods of Balashevich et al., 2000 that were developed for the problems of optimal control with the bounded initial state is not fixed are considered.