Controllability And Iterative Learning Control Of Conformable Fractional Differential Systems

Conformable fractional derivative is an extension of classical derivative,which has good properties in line with Leibniz rule and Chain rule,and can be used to describe some Newtonian mechanics and mathematical biology models.This dissertation mainly studies the controllability and iterative learning control of differential systems with conformable fractional derivatives.Firstly,drawing on the controllability research methods of classical linear systems,the Gramian criterion and rank criterion of conformable fractional order linear systems are given.On this basis,using Krasnoselskii fixed point theorem,the sufficient conditions for controllability of conformable fractional order nonlinear system and the corresponding control function solving method are given.Secondly,aiming at the problem of finite time trajectory complete tracking con-trol of conformable fractional order linear and nonlinear systems,the D-type,P-type,D?-type and PI?D?-type learning control laws are designed by using iterative learning control technology,and the convergence results of system tracking error in the sense of appropriate norm are given.Thirdly,the effectiveness of the theoretical results is verified by examples,and the tracking error numerical simulation is realized by MATLAB.