OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS

作     者：陈斌 Sergey A.TIMOSHIN Bin CHEN;Sergey A.TIMOSHIN

作者机构：Fujian Province University Key Laboratory of Computational ScienceSchool of Mathematical SciencesHuaqiao UniversityQuanzhou 362021China Matrosov Institute for System Dynamics and Control TheoryRussian Academy of SciencesLermontov str134664033 IrkutskRussia 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2022年第42卷第1期

页      面：283-298页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 0805[工学-材料科学与工程（可授工学、理学学位）] 070105[理学-运筹学与控制论] 0704[理学-天文学] 081101[工学-控制理论与控制工程] 0701[理学-数学] 071101[理学-系统理论] 0811[工学-控制科学与工程] 

基　　金：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) Scientific Research Funds of Huaqiao University(605-50Y 19017,605-50Y14040) 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") 

主　　题：optimal control problem hysteresis biological diffusion models nonconvex integrands nonconvex control constraints 

摘      要：This paper addresses a nonlinear partial differential control system arising in population *** system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or *** equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical *** study the problem of minimization of a given integral cost functional over solutions of the above *** 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 *** relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.