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«THE BULLETIN OF IRKUTSK STATE UNIVERSITY». SERIES «MATHEMATICS»
«IZVESTIYA IRKUTSKOGO GOSUDARSTVENNOGO UNIVERSITETA». SERIYA «MATEMATIKA»
ISSN 1997-7670 (Print)
ISSN 2541-8785 (Online)

List of issues > Series «Mathematics». 2025. Vol 54

On Optimal Control Problems with Active Infinite Horizon

Author(s)

Dmitry V. Khlopin1, Anton O. Belyakov2,3

1 Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, Russian Federation 

2 Lomonosov Moscow State University, Russian Federation 

3 National University of Science and Technology “MISIS”, Russian Federation

Abstract
The article proposes a new formulation of the optimal control problem on an infinite horizon. Usually in such problems, if a Bolza type problem is considered, then its terminal cost depends only on the initial state, additionally, one or another asymptotic requirement can be presented to the right end of the system. A feature of the proposed formulation is the ability to set control not only as a function of time, but also to choose an action-control at the completion of the process itself. This is primarily interesting from the point of view of economic applications, since it is the endless postponement of a generally unprofitable action (for example, ”debt repayment”) that often leads to a lack of optimal control. In addition to this new formulation, some necessary optimality conditions for the case of the simplest dynamics are presented. With these conditions the example of optimizing consumption under various borrowing restrictions is investigated.
About the Authors

Dmitry V. Khlopin, Cand. Sci. (Phys.–Math.), Krasovskii Institute of Mathematics and Mechanics UB RAS, Yekaterinburg, 620208, Russian Federation, khlopin@imm.uran.ru

Anton O. Belyakov, Cand. Sci. (Phys.Math.), Cand. Sci. (Econ.), Lomonosov Moscow State University, Moscow, 119991, Russian Federation, belyakov@mse-msu.ru

For citation
Khlopin D. V., Belyakov A. O. On Optimal Control Problems with Active Infinite Horizon. The Bulletin of Irkutsk State University. Series Mathematics, 2025, vol. 54, pp. 64–77. https://doi.org/10.26516/1997-7670.2025.54.64
Keywords
infinite horizon control problem, active infinite horizon, Pontryagin maximum principle, weakly overtaking optimality Acknowledgements
UDC
517.977
MSC
49K15, 91B62
DOI
https://doi.org/10.26516/1997-7670.2025.54.64
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