Adaptive ILC algorithms of nonlinear continuous systems with non-parametric uncertainties for non-repetitive trajectory tracking

Abstract

In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.

Keywords:

• adaptive iterative learning control
• non-repetitive trajectory tracking
• nonlinear continuous systems
• non-parametric uncertainties

Additional information

Funding

This work is supported in part by the National Natural Science Foundation (NNSF) of China [grant number U1135005].

Notes on contributors

Xiao-Dong Li

Xiao-Dong Li received the BS degree from the Department of Mathematics, Shaanxi Normal University, Xian, China, in 1987, the MPhil degree from the Nanjing University of Science and Technology, Nanjing, China, in 1990, and the PhD degree from the City University of Hong Kong, Hong Kong, in 2007. He is currently a professor in the School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China. His research interests include 2-D system theory, iterative learning control and artificial intelligence.

Mang-Mang Lv

Mang-Mang Lv received the BS degree from the Sun Yat-sen University, Guangzhou, China, in 2010. At present, he is pursuing his MPhil degree from the School of Information Science and Technology, Sun Yat-sen University, Guangzhou, China. His research interests include 2-D system theory and iterative learning control.

John K. L. Ho

John K. L. Ho received the BSc and MSc degrees in computer, control engineering from the Coventry University and PhD degree from the University of East London, UK. He has many years design experience in the field of automation when he was working in GEC Electrical Projects Ltd in UK. Currently, he is an associate professor in the Department of Mechanical and Biomedical Engineering, City University of Hong Kong. His research interests are in the fields of control engineering, enterprise automation and product design.