Studies On Optimal Control And Feedback Control Problems Of Several Kinds Of Ecological Models

This thesis mainly focuses on studies of optimal control and feedback control problems of several kinds of ecological models,and its main contents are related to the parameter estimation of an SIS epidemic model based on optimal control method-s,the optimal control of an integrated pest management model,the optimal harvest-ing of a stochastic competitive Lotka-Volterra population system with Levy jumps and feedback controls of a novel stochastic plankton ecosystem.The thesis consists of six chapters.Chapter one begins with the introduction of the history background and the source of ecological control,and then the current situation and development trend of ecological problems and control issues related to this thesis are reviewed and the main contents of this thesis are briefly summarized.Chapter two investigates the parameter estimation of an SIS epidemic model.By setting an appropriate performance index functional and regarding the estimated parameters in the model as control variables,the original problem is approximate-ly transformed into an optimal control problem.The existence and the first order necessary condition of the optimal control are all established,and the local unique-ness and stability of the parameter estimation obtained by optimal control methods are proved.That is,when observed data fluctuate in a small range,the estimation errors of parameters can be controlled by the observation errors.In this chapter,the parameter estimation problem of an SIS epidemic model governed by nonlinear reaction-diffusion equations is investigated by combining the methods employed in existing literature.The results provide a theoretical basis for estimating the basic reproductive number of the epidemic model.Chapter three considers the optimal control problem of a novel pest manage-ment model.The existence and uniqueness of the global positive solution to the corresponding model are first proved,and then the existence of optimal control for the corresponding control problem is proved and the first and two order necessary conditions of optimal control are established.The optimal control of a more general pest management model is studied in this chapter.The results obtained in this chapter are novel and of certain reference values for the effective prevention and control of pests and the scientific development of ecological agriculture.Chapter four discusses the optimal harvesting problem of a stochastic Lotka-Volterra system subject to Levy noises and white noises together.For the optimal harvesting problem,a verification theorem for the optimal harvesting strategy is giv-en,the monotonicity and upper bounds of the value function are all discussed in detail.An e-optimal harvesting strategy is established for those control problems with no exact optimal control.In this chapter,some results obtained in existing lit-erature are generalized to a more general ecological model.The results obtained in this chapter are novel and of certain values for efficient utilization and optimization of ecological resources.Chapter five puts emphasis on the feedback control of a three species plank-tonic ecosystem with environmental switching considered,where the switching law of environment is described by a partially observable Markov chain.Estimating the corresponding Markov chain by Wonham filtering,the original partial observable system is approximated by a fully observable system.The existence,uniqueness,stochastic boundedness and continuity of sample path of the positive solution to the fully observable system are investigated and the feedback controls to make the sys-tem be permanent or extinct are designed.The results obtained in this chapter are all novel and have some values for the effective regulation of the corresponding aquatic ecosystem.Chapter six is concerned with brief summary and research prospects.