Control Design On Singular Distributed Parameter System With Parabolic-elliptic Type And Ecological Application

With the development of science and technology,modern industrial processes have become increasingly complex.Especially in the complexity of spatial dimensions,based on distributed parameter system(DPS),there arise many singular distributed parameter systems(SDPS).Classical DPS theory and control method fail to meet such complex con-trol system.Based on the operator spectrum theory of partial differential equation(PDE)and singular system theory,for a class of parabolic-elliptic SDPS,the well-posedness,stability and observer design problems are considered in this dissertation.And also the application on ecological system and building automatic temperature control system are considered.The major work includes the following:Chapters 1,2 summarize the development and main research methods in SDPS liter-atures and give some symbols assumptions and preliminaries about the considered prob-lem.Chapter 3 investigates the regularization problem of SDPS.Inspired by equivalent form classification of singular systems,by using the characteristic line theory of PDE,for the first order linear SDPS,it can be classified by the generalized characteristic equation into several types,such as hyperbolic,parabolic and elliptic etc.This can be a generaliza-tion of the classification first order linear PDE.For the second order linear SDPS,there exist three reversible transformations:spatiotemporal coordinate transformation,struc-ture transformation,state variable transformation.With these three transformations the regularization of SDPS system is considered.In chapter 4,the well-posed problem and state response representation of linear SDP-S are studied.First,by the operator spectrum theory of PDE,the original SDPS system is transformed into infinite dimensional singular systems family(SSF).After the regulariza-tion of the target singular systems family,the explicit series expression of spatiotemporal state variable vector is obtained.Under the condition of convergency,the well-posed problem is studied and the admissible property of SSF is also considered.In chapter 5,under the influence of human population distribution,the boy-ciana-fish ecological system is considered.First,the system can be described as a nonlinear SDPS with Neumann boundary conditions and ratio-dependent functional re-sponse.Second,we examine the system’s persistence properties:the loacl stabilities of positive steady states,the absorbtion region and the global stability.And the proposed ap-proach is illustrated by numerical simulation.Finally,by using the realistic data collected in the past fourteen years,the SDPS parameter optimization model is built to predict the boyciana population.In chapter 6,the problem of state observation is addressed for SDPS with parabolic-elliptic type.For the nonhomogeneous boundary conditions,the generalized observer of SDPS is defined.Inspired from the backstepping observer method,a quite different ob-server with homogeneous integral transformation is built.On the one hand,times varying two sides boundary inputs are transformed into homogeneous boundary inputs.On the other hand,the two side boundary controller is changed into one state input controller which provides a basis for the state observer design.Consequently,the state observer is designed and the exponential stability of the error SDPS is investigated with SDPS theory.As an application,the state observation of distributed building automatic temperature con-trol process is considered.The simulation results show the effectiveness of the provided design.Finally,the results of the dissertation are summarized and further research topics are pointed out.