An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems  

作　　者：Jianming Wei Youan Zhang Hu Bao 

机构地区：[1]School of Weaponry Engineering, Naval University of Engineering [2]College of Engineering, Yantai Nanshan University [3]Aeronautical College, Yantai Nanshan University

出　　处：《IEEE/CAA Journal of Automatica Sinica》2018年第2期618-627,共10页自动化学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(60674090);Shandong Natural Science Foundation(ZR2017QF016)

摘　　要：This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control（AILC） scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control（ILC）, a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function（CEF）containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

关 键 词：Index Terms-Adaptive iterative learning control （AILC） boundary layer function composite energy function （CEF） frac-tional order differential learning law fractional order nonlinearsystems Mittag-Leffler function. 

分 类 号：TP2[自动化与计算机技术—检测技术与自动化装置]