The Optimal Control Problems For Two Classes Of Population Systems With Size-structure

The biological species are composed of individuals,and there are structural differences among individuals in physical size,age,gender and other aspects.For most species,it is more practical to study the control problems of population with size-structure than age-structure.On the one hand,size-structure can better describe some physiological characteristics of individuals.On the other hand,it can help as more accurately analyze the reproduction and viability of the population.Therefore,it has important theory meanings and practical application value to discuss the optimal control of population systems with size-structure.This paper mainly discusses the optimal control problems for two classes of population systems with size-structure.In the first chapter,the development history of the optimal control problems of population system is introduced.The research status of the optimal control problems with size-structure is also briefly introduced.In the second chapter,the optimal control for inputting rate of a size-structure competitive system is concerned.Firstly,the existence and uniqueness of the solution of the competitive system is proved with the help of the fixed point theorem.Secondly,the existence and uniqueness of the optimal control is obtained by the Ekeland variational principle.The necessary conditions of the optimal control are established by the conception of tangent and normal cone.In the third chapter,the optimal control problem for a size-structure mosquito population with diffusion is discussed.Firstly,the existence and uniqueness of the system is proved by using the fixed point theorem.Secondly.the existence and uniqueness of the optimal control is obtained by using Mazur's teorem,and the necessary conditions of the optimal control are established.