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Algorithm for Solving a Problem of Optimal Control of Structured Populations Interacting at Stationary States

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Abstract

We consider an optimal control problem with differential and integral constraints. The initial condition in the control system of ordinary differential equations has a nonlocal form; it is defined by the solution of the system. We develop and substantiate an algorithm for finding an optimal control maximizing the profit. The algorithm allows one to reduce the solution of the original problem to the solution of simpler optimal control problems related through one of the parameters of the model. We show that one can find a parameter value that determines the solution of the original problem, and we explain how to do this. The approach proposed allows one to efficiently solve optimization problems arising in models of control of structured populations interacting at stationary states.

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References

  1. A. A. Davydov and A. S. Platov, “Optimal stationary exploitation of size-structured population with intra-specific competition,” in Geometric Control Theory and Sub-Riemannian Geometry, Ed. by G. Stefani et al. (Springer, Cham, 2014), Springer INdAM Ser. 5, pp. 123–132.

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Funding

The research of A. S. Platov (Sections 3 and 4) was supported by the Russian Science Foundation under grant 19-11-00223.

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Authors and Affiliations

  1. International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, A-2361, Laxenburg, Austria

    A. A. Krasovskiy

  2. Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, 119991, Russia

    A. S. Platov

Authors
  1. A. A. Krasovskiy
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  2. A. S. Platov
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Corresponding author

Correspondence to A. A. Krasovskiy.

Additional information

Translated from Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 315, pp. 151–159 https://doi.org/10.4213/tm4232.

Translated by I. Nikitin

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Krasovskiy, A.A., Platov, A.S. Algorithm for Solving a Problem of Optimal Control of Structured Populations Interacting at Stationary States. Proc. Steklov Inst. Math. 315, 140–148 (2021). https://doi.org/10.1134/S0081543821050102

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  • DOI: https://doi.org/10.1134/S0081543821050102

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