Geodesic
Algorithm for Solving a Problem of Optimal Control of Structured Populations Interacting at Stationary States
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 151-159
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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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     title = {Algorithm for {Solving} a {Problem} of {Optimal} {Control} of {Structured} {Populations} {Interacting} at {Stationary} {States}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
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A. A. Krasovskiy; A. S. Platov. Algorithm for Solving a Problem of Optimal Control of Structured Populations Interacting at Stationary States. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Optimal Control and Differential Games, Tome 315 (2021), pp. 151-159. http://geodesic.mathdoc.fr/item/TM_2021_315_a9/

[1] Davydov A.A., Platov A.S., “Optimal stationary exploitation of size-structured population with intra-specific competition”, Geometric control theory and sub-Riemannian geometry, Springer INdAM Ser., 5, ed. by G. Stefani et al., Springer, Cham, 2014, 123–132 | DOI

[2] Murphy L.F., “A nonlinear growth mechanism in size structured population dynamics”, J. Theor. Biol., 104:4 (1983), 493–506 | DOI

[3] A. A. Panesh and A. S. Platov, “Optimization of size-structured populations with interacting species”, J. Math. Sci., 188:3 (2013), 293–298 | DOI | MR

[4] L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes, Pergamon, Oxford, 1964