Abstract
The paper is devoted to the optimal control problem which is based on the model of optimization of resources productivity. Model analysis is implemented within the framework of Pontryagin maximum principle for the problems with infinite time horizon. Qualitative analysis of the Hamiltonian system allows to formulate necessary and sufficient conditions of existence of a steady state in terms of the model parameters. Under these conditions and an assumption on the saddle character of the steady state, we construct a nonlinear regulator which allows to approximate optimal trajectories by the solutions of the stabilized Hamiltonian system at a vicinity of the steady state. Finally, comparative analysis of results of numerical simulations is carried out.
This work was supported by RFBR (Projects 11-01-00427-a, 12-01-00024-a, 12-01-31300), by the Program for Sponsorship of Leading Scientific Schools (Project NSCH-64508.2010.1), by Programs of the Presidium of the Russian Academy of Sciences (Projects 12-Π-1-1002, 12-Π-1-1012, 12-Π-1-1038, 12-Π-7-1001), by the Project 13-1-HΠ-253 of the Ural Branch Of RAS, and the International Institute for Applied Systems Analysis (Project NSFC-IIASA).
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Usova, A.A., Tarasyev, A.M. (2015). Optimal Control Problem on Optimization of Resources Productivity. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_18
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DOI: https://doi.org/10.1007/978-3-319-12577-0_18
Publisher Name: Birkhäuser, Cham
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