ПОСТРОЕНИЕ ОПТИМАЛЬНЫХ ТРАЕКТОРИЙ ИНТЕГРИРОВАНИЕМ ГАМИЛЬТОНОВОЙ ДИНАМИКИ В МОДЕЛЯХ ЭКОНОМИЧЕСКОГО РОСТА ПРИ РЕСУРСНЫХ ОГРАНИЧЕНИЯХ

科研成果: Article

摘要

The paper is devoted to an optimal control problem based on a model of optimization of natural resource productivity. The analysis of the problem is conducted with the use of Pontryagin's maximum principle adjusted to problems with infinite time horizon. Properties of the Hamiltonian function are investigated. Based on methods for resolving singularities, a special change of variables is suggested, which allows to simplify essentially the solution of the problem by means of analyzing steady states and corresponding Jacobian matrices of the Hamiltonian system. An important property of the change of variables is the possibility of an adequate and meaningful economic interpretation of the new variables. The existence of steady states of the Hamiltonian dynamics in the domain of transient control regime is studied, and a stable manifold is constructed for finding boundary conditions of integration of the Hamiltonian system in backward time. On the basis of the implemented analysis, an algorithm is proposed for constructing optimal trajectories under resource constraints. The analysis of the algorithm provides estimates for its convergence time and for its error with respect to the utility functional of the control problem based on the properties of the Hamiltonian system and constraints of the model. The asymptotic behavior of optimal trajectories is studied with the use of the implemented research. The operation of the algorithm is illustrated by graphical results.
投稿的翻译标题Optimal trajectory construction by integration of Hamiltonian dynamics in models of economic growth under resource constraints
源语言Russian
页(从-至)258-276
页数19
期刊Труды института математики и механики УрО РАН
20
4
Published - 2014

GRNTI

  • 27.00.00 MATHEMATICS

Level of Research Output

  • VAK List

指纹 探究 'ПОСТРОЕНИЕ ОПТИМАЛЬНЫХ ТРАЕКТОРИЙ ИНТЕГРИРОВАНИЕМ ГАМИЛЬТОНОВОЙ ДИНАМИКИ В МОДЕЛЯХ ЭКОНОМИЧЕСКОГО РОСТА ПРИ РЕСУРСНЫХ ОГРАНИЧЕНИЯХ' 的科研主题。它们共同构成独一无二的指纹。

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