Controllability Of Several Classes Of Fractional Differential Systems

In recent years,fractional differential systems which have developed rapidly were applied in the fields of optics,mechanics,signal processing,system identification,control,robot and so on.Based on this situation,the controllability of several kinds of nonlinear differential systems by using relevant knowledge and control theory were studies in this work.The thesis is divided into six chapters.In Chapter 1,the research background of related differential equations,the current situation at home and abroad,and the main work of this paper are briefly introduced.In Chapter 2,we introduce the preliminary knowledge needed in this paper,including set-valued mapping,function space,the definition of fractional calculus,operator semigroups and related theorems.In Chapter 3,the feedback control problem for a class of Hilfer fractional differential inclusions with history dependent operators is studied.Firstly,the prior estimate of the solution of the fractional feedback control system is given,and then the existence of the fractional feedback control system is proved by using Bohnenblast-Karlin fixed point theorem.Finally,the optimal control problem of fractional feedback control system is considered and its solvability is established.In Chapter 4,we study the approximate controllability of Hilfer fractional impulsive differential equations in Banach spaces.Firstly,the existence of the solution is derived from the operator semigroup theory,then the uniqueness of the solution is obtained through a set of assumptions,and finally the approximate controllability of the impulsive system is proved.In Chapter 5,the approximate controllability of control systems with time delay is studied.Firstly,the properties of mild solution are derived,then the relevant linear operator is defined,and finally the approximate controllability of the system is proved by sequence method.In Chapter 6,we summarize the current research work and put forward future research ideas.