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ON A METHOD OF SUCCESSIVE APPROXIMATIONS FOR THE SOLUTION OF OPTIMAL CONTROL PROBLEMS,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OH
The determination of optimal control for a process, which is described by a system of ordinary differential equations of the nth order, is reduced to a boundary value problem for a system of equations of the 2nth order. The solution of boundary value problems for complex non-linear systems often encounters significant computational difficulties and re quires a large expenditure of machine time. Theorefore, methods of solving optimal control problems, which permit the circumvention of these difficulties, are presented for considera tion. A method of successive approximations, which is based on the maximal principle, is proposed for the determination of optimal control in problems with an open right limit. Author
Trans. from Zhurnal Vychislitel'noy Matematiki I Matematicheskoy Fiziki, 2:6, pp. 1132-1139, 1962.