Minimax Theory and its Applications 05 (2020), No. 2, 455--470
Copyright Heldermann Verlag 2020
Approximate Optimal Control in the Infinite Time Horizon Problem with Phase Constraints
Anastasiia A. Usova
Krasovskii Institute of Mathematics and Mechanics, Russian Academy of Sciences, Ural Branch, 620108 Yekaterinburg, Russia
ausova@imm.uran.ru
Alexander M. Tarasyev
Yeltsin Ural Federal University, 620002 Yekaterinburg, Russia
tam@imm.uran.ru
The paper investigates a control problem of optimal distribution of investments directed towards improvement of the resource productivity and/or purchasing the natural resources. The problem is based on the growth model of the effective resource consumption under the condition on resources' exhaustion. The paper provides an interpretation of phase variables in terms of the reliability theory. The optimal solution of the problem is approximated by piecewise constant controls that guarantee convergence of the trajectories to the unique equilibrium of the Hamiltonian system. The derived approximation satisfies the phase constraints and matches with the stabilized solutions constructed on the basis of the nonlinear regulator approach.
Keywords: Optimal control problem, phase constraints, reliability theory, piecewise constant controls, Hamiltonian system, growth models.
MSC: 93C10, 49M25, 34H05, 35F21.
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