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Abstract
This paper is a summary of the research development in the rational (total) nonlinear dynamic modelling over the last two decades. Total nonlinear dynamic systems are defined as those where the model parameters and input (controller outputs) are subject to nonlinear to the output. Previously, this class of models has been known as rational models, which is a model that can be considered to belong to the nonlinear autoregressive moving average with exogenous input (NARMAX) model subset and is an extension of the well-known polynomial NARMAX model. The justification for using the rational model is that it provides a very concise and parsimonious representation for highly complex nonlinear dynamic systems and has excellent interpolatory and extrapolatory properties. However, model identification and controller design are much more challenging compared to the polynomial models. This has been a new and fascinating research trend in the area of mathematical modelling, control, and applications, but still within a limited research community. This paper brings several representative algorithms together, developed by the authors and their colleagues, to form an easily referenced archive for promotion of the awareness, tutorial, applications, and even further research expansion.
Acknowledgements
The authors are grateful to the editors and the anonymous reviewers for their helpful comments and constructive suggestions with regard to the revision of the paper.
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Notes on contributors
Quanmin Zhu
Quanmin Zhu is professor in Control Systems at Faculty of Environment and Technology, University of the West of England, Bristol, UK. He obtained his MSc degree from Harbin Institute of Technology, China in 1983 and PhD degree from Faculty of Engineering, University of Warwick, UK in 1989. His main research interest is in the area of nonlinear system modelling, identification, and control. His other research interests are in investigating electrodynamics of acupuncture points and sensory stimulation effects in human body, modelling of human meridian systems, and building up electro-acupuncture instruments. Currently, Professor Zhu is acting as a member of Editorial Committee of Chinese Journal of Scientific Instrument, an editor (and founder) of International Journal of Modelling, Identification and Control, and an editor of International Journal of Computer Applications in Technology.
Yongji Wang
Yongji Wang received the undergraduate degree in electrical engineering from Shanghai Railway University, Shanghai, P.R. China, the MS degree and the PhD degree in automation from Huazhong University of Science and Technology, Wuhan, P.R. China, in 1982, 1984, and 1990, respectively. He has been with Huazhong University of Science and Technology, Wuhan, P.R. China, since 1984, where he is currently a professor of Control Engineering. His main interest is in intelligent control and autonomous mobile robot, and he has done research in neural network control, predictive control, adaptive control, and most recently, flight vehicle optimal control. Dr. Wang is a member of IEEE, the president of Hubei Automation Association, China, a member of council of the Chinese Automation Association, standing member of council of Intelligent Robot Committee of Chinese Artificial Intelligence Society. He is a regional editor (Asia and Pacific) of International Journal of Modelling Identification and Control.
Dongya Zhao
Dongya Zhao received BEng degree from Shandong University, Jinan, China, in 1998, MSc degree from Tianhua Institute of Chemical Machinery & Automation, Lanzhou, China, in 2002, and PhD degree from Shanghai Jiao Tong University, Shanghai, China, in 2009. He was a research fellow in Nanyang Technological University during July 2011 to July 2012. Since 2002, he has been with College of Chemical Engineering, China University of Petroleum, where he is currently an associate professor. His research interests include robot control, sliding mode control, process modelling and control, and nonlinear system control and analysis.
Shaoyuan Li
Shaoyuan Li received the PhD degree from the Department of Computer and System Science, Nan Kai University, in 1997. He was a lecturer in the Department of Electrical Engineering, Hebei University of Technology, Tianjin from 1994 to 1998, and was with Department of Automation, Shanghai Jiao Tong University as the postdoctoral research fellow from 1998 to 2000. Since then, he has been with the Department of Automation, Shanghai Jiao Tong University, China, and he is currently a full professor in this department, and in charge of the head of this department from 2004 to 2013. His research interests cover system identification and controller tuning, adaptive control, satisfying optimization and predictive control, and so on. He is the author or co-author of four monographs and about 200 technical papers.
Stephen A. Billings
Stephen A. Billings is a professor in the Department of Automatic Control and Systems Engineering, University of Sheffield, UK, and leads the Signal Processing and Complex Systems research group. His research interests include system identification and information processing for nonlinear systems, NARMAX methods, model validation, prediction, spectral analysis, adaptive systems, nonlinear systems analysis and design, neural networks, wavelets, fractals, machine vision, cellular automata, spatio-temporal systems, fMRI and optical imagery of the brain, synthetic biology, and related fields.