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Optimal Control and Positional Controllability in a One-Sector Economy

Author

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  • Nikolai Grigorenko

    (Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119992 Moscow, Russia)

  • Lilia Luk’yanova

    (Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119992 Moscow, Russia)

Abstract

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations.

Suggested Citation

  • Nikolai Grigorenko & Lilia Luk’yanova, 2021. "Optimal Control and Positional Controllability in a One-Sector Economy," Games, MDPI, vol. 12(1), pages 1-12, February.
    • Handle: RePEc:gam:jgames:v:12:y:2021:i:1:p:11-:d:490661
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    References listed on IDEAS

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    1. Dieter Grass & Jonathan P. Caulkins & Gustav Feichtinger & Gernot Tragler & Doris A. Behrens, 2008. "Optimal Control of Nonlinear Processes," Springer Books, Springer, number 978-3-540-77647-5, December.
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    Cited by:

    1. Ellina Grigorieva, 2021. "Optimal Control Theory: Introduction to the Special Issue," Games, MDPI, vol. 12(1), pages 1-4, March.
    2. Veniamin Mokhov & Sergei Aliukov & Anatoliy Alabugin & Konstantin Osintsev, 2023. "A Review of Mathematical Models of Macroeconomics, Microeconomics, and Government Regulation of the Economy," Mathematics, MDPI, vol. 11(14), pages 1-37, July.

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