Controllability For Several Classes Of Nonlinear Fractional Dynamical Systems

This thesis investigates the controllability for several classes of nonlinear fractional dynamical systems by applying the knowledge and control theory of fractional calculus and Hilfer fractional derivative.The structure of this thesis is as follows:In chapter 1,we briefly introduce the research background of related problems,the domestic and foreign research situation and the main work of this thesis.In chapter 2,we recall the preliminaries necessary for the study of this thesis,including symbol description,function space,fractional calculus definition and related lemma,setvalued mapping and operators semigroup theory.In chapter 3,we study optimal feedback control of system governed by fractional delay equations involving Caputo derivatives.On the basis of previous work,we add the delay term to extend the existing theoretical results.The existence of the system solution is obtained mainly through Gronwall inequality and Leray-Schauder alternative fixed point theorem.Secondly,the existence of feasible pairs is obtained by using Filippove theorem and Cesari property.Then,we prove the existence result of optimal control pairs for a Lagrange problem.Finally,we give an example analysis and application of the main results.In chapter 4,the feedback control theory of Caputo or Riemann-Liouville impulsive equation has been relatively mature in recent years and the theory result is fruitful.However,the impulsive feedback control of Hilfer fractional derivatives is still untreated topic in the literature.Therefore,the emphasis of this chapter is to study the impulsive feedback control systems of Hilfer fractional derivative in separable reflexive Banach space through semigroup theory and Filippove theorem,and finally give the application of impulse differential variational inequality.In chapter 5,we study the approximation controllability of impulsive Hilfer fractional equations.Firstly,the existence and uniqueness of solutions for the systems are obtained by applying the Banach fixed point theorem,and then the approximation controllability of the system is proved.In the end,we give a conclusion of our present work and introduce some further study ideas in the future.