OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS  

作　　者：Bin CHEN Sergey A.TIMOSHIN 陈斌;Sergey A.TIMOSHIN(Fujian Province University Key Laboratory of Computational Science,School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China;Matrosov Institute for System Dynamics and Control Theory,Russian Academy of Sciences,Lermontov str,134,664033 Irkutsk,Russia)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2022年第1期283-298,共16页数学物理学报（B辑英文版）

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")。

摘　　要：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 relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

关 键 词：optimal control problem HYSTERESIS biological diffusion models nonconvex integrands nonconvex control constraints 

分 类 号：O232[理学—运筹学与控制论]