OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

doi:10.1007/s10473-022-0116-x

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (1): 283-298.doi: 10.1007/s10473-022-0116-x

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OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

Bin CHEN¹, Sergey A. TIMOSHIN^1,2

1. Fujian Province University Key Laboratory of Computational Science, School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, China;
2. Matrosov Institute for System Dynamics and Control Theory, Russian Academy of Sciences, Lermontov str. 134, 664033, Irkutsk, Russia

Received:2020-06-15 Revised:2020-10-21 Online:2022-02-25 Published:2022-02-24
Contact: Sergey A. TIMOSHIN,E-mail:sergey.timoshin@gmail.com E-mail:sergey.timoshin@gmail.com
Supported by:
This work was supported by National Natural Science Foundation of China (12071165 and 62076104), Natural Science Foundation of Fujian Province (2020J01072), Program for Innovative Research Team in Science and Technology in Fujian Province University, Quanzhou High-Level Talents Support Plan (2017ZT012), and by Scientific Research Funds of Huaqiao University (605-50Y19017, 605-50Y14040). The research of the second author was also supported by Ministry of Science and Higher Education of Russian Federation (075-15-2020-787, large scientific project "Fundamentals, methods and technologies for digital monitoring and forecasting of the environmental situation on the Baikal natural territory").

Abstract

Abstract: This paper addresses a nonlinear partial differential control system arising in population dynamics. The system consist of three diffusion equations describing the evolutions of three biological species:prey, predator, and food for the prey or vegetation. The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process. We study the problem of minimization of a given integral cost functional over solutions of the above system. The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable. Some relaxation-type results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

Key words: optimal control problem, hysteresis, biological diffusion models, nonconvex integrands, nonconvex control constraints

CLC Number:

49J20

Bin CHEN, Sergey A. TIMOSHIN. OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS[J].Acta mathematica scientia,Series B, 2022, 42(1): 283-298.

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OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

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