Abstract:
We study the problem of optimizing the harvesting of a renewable resource distributed on a circle. The dynamics of the resource restoration process is described by a Kolmogorov–Petrovskii–Piskunov–Fisher type equation in divergence form, and the harvesting of the resource is performed by a machine that moves cyclically along the circle. The objective functional is an average quantity depending on the position of this machine, the difficulty of detecting or harvesting the resource from this position, and the distance of the resource from this position. We prove that there exists an optimal motion of the harvesting machine that maximizes the average time profit in the natural form in the long run when the initial distribution of the resource is not less than the limit value in the absence of harvesting.
Citation:
A. O. Belyakov, A. A. Davydov, “Optimal Cyclic Harvesting of a Distributed Renewable Resource with Diffusion”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 64–73; Proc. Steklov Inst. Math., 315 (2021), 56–64
\Bibitem{BelDav21}
\by A.~O.~Belyakov, A.~A.~Davydov
\paper Optimal Cyclic Harvesting of a Distributed Renewable Resource with Diffusion
\inbook Optimal Control and Differential Games
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 315
\pages 64--73
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4246}
\crossref{https://doi.org/10.4213/tm4246}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 315
\pages 56--64
\crossref{https://doi.org/10.1134/S0081543821050059}
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Linking options:
https://www.mathnet.ru/eng/tm4246
https://doi.org/10.4213/tm4246
https://www.mathnet.ru/eng/tm/v315/p64
This publication is cited in the following 3 articles:
A. A. Davydov, A. S. Platov, D. V. Tunitskii, “Suschestvovanie optimalnogo statsionarnogo resheniya v KPP-modeli pri nelokalnoi konkurentsii”, Tr. IMM UrO RAN, 30, no. 3, 2024, 113–121
A. A. Davydov, A. S. Platov, D. V. Tunitsky, “Existence of an Optimal Stationary Solution in the KPP Model under Nonlocal Competition”, Proc. Steklov Inst. Math., 327:S1 (2024), S66
A. Davydov, E. Vinnikov, “Optimal cyclic dynamic of distributed population under permanent and impulse harvesting”, Dynamic Control and Optimization, Springer Proceedings in Mathematics & Statistics, 407, 2022, 101