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Article

Optimal Control and Positional Controllability in a One-Sector Economy

Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119992 Moscow, Russia
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Author to whom correspondence should be addressed.
Academic Editor: Ellina Grigorieva
Received: 26 November 2020 / Revised: 8 January 2021 / Accepted: 20 January 2021 / Published: 1 February 2021
(This article belongs to the Special Issue Optimal Control Theory)
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. View Full-Text
Keywords: ramsey model; nonlinear control system; Pontryagin maximum principle; switching function; bang-bang control; singular arc of the third order; positional control ramsey model; nonlinear control system; Pontryagin maximum principle; switching function; bang-bang control; singular arc of the third order; positional control
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MDPI and ACS Style

Grigorenko, N.; Luk’yanova, L. Optimal Control and Positional Controllability in a One-Sector Economy. Games 2021, 12, 11. https://0-doi-org.brum.beds.ac.uk/10.3390/g12010011

AMA Style

Grigorenko N, Luk’yanova L. Optimal Control and Positional Controllability in a One-Sector Economy. Games. 2021; 12(1):11. https://0-doi-org.brum.beds.ac.uk/10.3390/g12010011

Chicago/Turabian Style

Grigorenko, Nikolai, and Lilia Luk’yanova. 2021. "Optimal Control and Positional Controllability in a One-Sector Economy" Games 12, no. 1: 11. https://0-doi-org.brum.beds.ac.uk/10.3390/g12010011

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