Controllability For Several Classes Of Nonlinear Impulsive Differential Systems

In recent years,the controllability of impulsive differential systems has attracted people's attention,and such systems have been applied in aerospace technology,information science,control system,communication,life science,medicine,economy and other fields.For this reason,the controllability of several classes of nonlinear impulsive differential systems is studied in this thesis.The structure of this thesis is as follows:In chapter 1,the introduction simply introduces the research background of the related issues studied,the domestic and foreign research situation and the main work required of this thesis.In chapter 2,the preliminaries include function space,fractional calculus definition and related lemmas,set-valued mappings and operator semigroup theory.In chapter 3,The approximation controllability of a class of nonlinear fractional or-der impulsive differential systems is considered in Banach space.Some achievements have been made on the approximation controllability of semilinear differential systems,but the ap-proximation controllability of impulsive differential systems is of more practical significance.The existence of the system mild solution is obtained mainly through Schauder fixed point theorem.Secondly,the approximation controllability results is obtained by using the rele-vant properties of the?-order solution operator{T_?(t)}_t?0and the?-order resolvent operator{S_?(t)}_t?0.Finally,we give an example analysis and application of the main results.In chapter 4,the approximation controllability of a class of nonlocal fractional order im-pulsive differential systems with time delay is considered in Hilbert space.The approximation controllability theory of Caputo or Riemann-Liouville impulsive equation has been relatively mature in recent years and the theory result is fruitful.However,due to the problems in the reality,we have to consider about the approximation controllability of nonlocal impulsive dif-ferential systems with time delay.Finally,we give an example analysis and application of the main results.In chapter 5,a class of nonlinear fractional delay control feedback control systems is considered in separable reflexive Banach space.First,the existence and uniqueness of the mild solution of the system are obtained by the Banach fixed point theorem and the Schauder fixed point theorem.Then,the optimal feedback control is obtained by the semigroup theory and the Filippove theorem.Finally give the application of impulse differential variational inequality.Finally,I will summarize the current research results,and propose research ideas in the future research process.