| Recently, the controllability of the dynamic systems has received comprehensive re-search and applications on the area of biology, physical, finance, medicine etc. For this reason,based on the knowledge and control theory of fractional calculus, we discussed the control theorem for several classes of fractional differential systems in this thesis.This thesis consists of six chapters:Chapter 1 introduces the background, the domestic and foreign research situation of frac-tional differential equations, impulsive differential equations and control theory and presents the main work of this thesis.Chapter 2 recalls the preliminaries necessary which will be used in this thesis, including some definitions, properties of fractional calculus and conclusions of function spaces, Borel measure, as well as the set valued mapping theorems which are helpful in our study.Chapter 3 is deal with the controllability of linear and nonlinear Caputo impulsive frac-tional order damped systems. Our main purpose is to establish some necessary and sufficien-t conditions for controllability for this kind of impulsive control systems by using Mittag-Leffler matrix functions and Schauder fixed point theorem.Chapter 4 is mainly concerned with feedback control systems governed by fractional evolution equations. On the basis of previous work, By using the Filippove theorem and some related lemmas, we considered the optimal control of the Lagrange type problem.Chapter 5 discuss the feedback control systems governed by fractional neutral equations involving Riemann-Liouville derivatives. The existence and uniqueness result of solutions for the feedback control systems are obtained by applying the Schaefer’s fixed point theorem.by using the Filippove theorem, we prove the nonempty of feasible pairs. At the end of the chapter, we discuss the existence of the optimal control pairs for Lagrange type problems.Chapter 6 gives a conclusion of our present work and make a plan for further research. |
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