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Оптимальное управление инвестициями в закрытой динамической модели трехсекторной экономики: математическая постановка задачи и общий анализ на основе принципа максимума
A mathematical optimal control problem formulated on the basis of the closed-form
dynamic problem of three-sector economy is studied. The system state is described
by a set of functions of specific capital in each sector; the control parameter is the
quantity characterizing a volume of specific investments of the fund-creating sector
playing a key role in the economic system. The mathematical problem is formulated
as a classical optimal control problem with a fixed time interval, with the fastened left
and free right trajectory ends. Solving the stated problem is based on the Pontryagin
maximum principle. A general control structure is determined that corresponds to the
maximum principle. A method for further study of the stated problem is described,
which consists in analytical determination of main and associated variables and in
development of the procedure for finding the optimal control.