Observability Of Polynomial Systems Based On Algebraic Methods

As a special category of nonlinear systems,polynomial systems exist in all aspects of daily life,such as aviation,medical care and electronics.Polynomial systems can be used as a basis for the research of most nonlinear systems.Therefore,Polynomial system controllability,observability,reachability and other basic characteristics of the study is particularly important.In recent years,the application of algebraic research methods to system theory has attracted more and more attention.More and more studies on the observability and reachability of polynomial systems have been developed.The research on polynomial system is more extensive than that of symbolic computation by means of numerical methods such as the sum of squares method.In this paper,we consider the previous research on the observability of polynomial systems for symbolic computation and derive its sufficient conditions.The full text is divided into five chapters:The first chapter is an introduction,briefly introducing the research background,significance and current situation of polynomial system research.The second chapter gives the preliminary knowledge about the definition and properties of polynomial rings,ideal,affine algebraic varieties involved in this paper,the related definitions,properties and algorithms of Grobner basic definitions,and the relations between ideal and affine algebraic clusters Make a whole introduction.The third chapter introduces the definition of observability in polynomial systems.By affine algebraic clusters and the properties of the ideals and the relations between them,the sufficient conditions for global observability of continuous polynomial systems are given and proved by examples.In the fourth chapter,based on the idea similar to the previous chapter,the sufficient conditions for the global observability of the discrete-time polynomial systems are deduced for the discrete polynomial system by applying the relation between polynomial ideal and affine algebraic clusters.The fifth chapter summarizes the work of this paper,points out the improvement of this paper and expounds the general prospect of further research in the future.