Iterative Learning Control For A Class Of Impulsive Differential Equations With Adaptive Derivatives

The conformable derivative is a generalization of the classical derivative,with good properties conforming to the Leibniz and the chain rule.The conformable differential equation is suitable for describing Newtonian mechanics and mathematical biological models,and is widely applicable to the field of physics and biology.This paper mainly studies two problems:One is the existence,uniqueness and Ulam stability of solutions of conformable impulsive differential equations.The other is to consider the iterative learning control of the controlled system on this basis.First,we derive the exact solution expressions of the homogeneous and non-homogeneous problems of linear equations.For nonlinear problems,under suitable conditions,Picard successive approximation method is used to prove the existence and uniqueness of the solution,and the Schauder fixed point theorem is used to prove the existence of the solution.Then,we analyze the Ulam-Hyers and Ulam-Hyers-Rassias stability of solutions.Secondly,the problem of finite-time tracking control of conformable impulsive differential equations is studied.We adopt iterative learning control technology to design-type and-type learning control laws for linear equations,and design-type learning control for nonlinear equations.We comprehensively use H¨older inequality and Gronwall's inequality and other techniques to give the convergence results of the tracking error in the sense of the appropriate norm.Finally,a numerical example verifies the validity of the theoretical results.