Attainable Sets Of Differential Inclusions

The research of differential inclusion started in the 1950 s.The theory of differential inclusion is of great help in solving the physical and engineering aspects,mainly using the uncertainty system model to study the practical problems.For a dynamic system,in the case of input bounded,the attainable sets is used to describe the possible ending state of system from the origin to the end.Therefore,it is of great practical significance to research the attainable sets of differential inclusion.This paper mainly studies the reachable sets of two kinds of differential inclusions,which are divided into the following aspects.Firstly,the research status and basic concepts of differential inclusion and attainable sets are introduced.Secondly,we present the knowledge of the functions used in this paper and the knowledge of set-valued mapping.Thirdly,the basic concepts of the attainable sets of differential inclusion and the related theorem are given,and the attainable sets of differential inclusion is obtained,then,the bounded value of the attainable sets of the first order differential inclusion is analyzed,The existence of the attainable sets boundary value,and an example is present for the of our results.Finally,we study the boundary value of attainable sets for the second order differential inclusion.We mainly use the relation between the optimal control system and the differential inclusion,and solve the attainable sets of the second order affine control system,to determine the boundary value of the attainable sets of second order differential inclusion,and then provide an example to illustrate the effectiveness of the method.