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A time/space separation based 3D fuzzy modeling approach for nonlinear spatially distributed systems

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Abstract

Spatially distributed systems (SDSs) are usually infinite-dimensional spatio-temporal systems with unknown nonlinearities. Therefore, to model such systems is difficult. In real applications, a low-dimensional model is required. In this paper, a time/space separation based 3D fuzzy modeling approach is proposed for unknown nonlinear SDSs using input-output data measurement. The main characteristics of this approach is that time/space separation and time/space reconstruction are fused into a novel 3D fuzzy system. The modeling methodology includes two stages. The first stage is 3D fuzzy structure modeling which is based on Mamdani fuzzy rules. The consequent sets of 3D fuzzy rules consist of spatial basis functions estimated by Karhunen-Love decomposition. The antecedent sets of 3D fuzzy rules are used to construct temporal coefficients. Going through 3D fuzzy rule inference, each rule realizes time/space synthesis. The second stage is parameter identification of 3D fuzzy system using particle swarm optimization algorithm. After an operation of defuzzification, the output of the 3D fuzzy system can reconstruct the spatio-temporal dynamics of the system. The model is suitable for the prediction and control design of the SDS since it is of low-dimension and simple nonlinear structure. The simulation and experiment are presented to show the effectiveness of the proposed modeling approach.

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Author information

Authors and Affiliations

  1. Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronics and Automation, Shanghai University, Shanghai, 200072, China

    Xian-Xia Zhang, Zhi-Qiang Fu & Bing Wang

  2. Institute of Automation, Shanghai Jiao Tong University, Shanghai, 200240, China

    Shao-Yuan Li

  3. Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, 110016, China

    Tao Zou

Authors
  1. Xian-Xia Zhang
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  2. Zhi-Qiang Fu
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  3. Shao-Yuan Li
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  4. Tao Zou
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  5. Bing Wang
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Corresponding author

Correspondence to Xian-Xia Zhang.

Additional information

This work was supported by National Science Foundation of China (Nos. 61273182, 31570998, 51375293 and 61374112).

Recommended by Associate Editor Mohammed Chadli

Xian-Xia Zhang received the B.Eng. degree in automatic control from the University of Science and Technology Beijing, China in 1998, received the M. Eng. degree in measurement techniques and instrumentation from Shanghai University, China in 2003, and received the Ph.D. degree in control theory and control engineering from Shanghai Jiao Tong University, China in 2008.

Her research interests include spatio-temporal system modeling, intelligent control for spatially distributed system, machine learning algorithm and vision based robot control.

Zhi-Qiang Fu received the B. Sc. degree in automatic control from the Nanchang Hangkong University, China, in 2014. He is currently a master student in School of Mechatronics and Automation, Shanghai University, China.

His research interests include spatiotemporal system modeling, intelligent control for spatially distributed system and machine learning algorithm.

Shao-Yuan Li received the B. Sc. and M. Sc. degrees in automation from Hebei University of Technology, China in 1987 and 1992, respectively, and received the Ph.D. degree from Department of Computer and System Science, Nankai University, China in 1997. Since July 1997, he has been with Department of Automation, Shanghai Jiao Tong University, China, where he is currently a professor.

His research interests include fuzzy systems, model predictive control, dynamic system optimization, and system identification.

Tao Zou received the B.Eng. degree in automatic control from Shenyang Institute of Chemical Technology, China in 1998, received the M.Eng. degree in control theory and control engineering from Shenyang Institute of Chemical Technology, China in 2001, and received the Ph.D. degree in control theory and control engineering from Shanghai Jiaotong University, China in 2005.

His research interests include real time optimization of industrial process and model predictive control theory and applications.

Bing Wang received the B.Eng. degree in precision mechanism and precision instrument from University of Science and Technology of China, China in 1989, received the M. Sc. degree in operations research and control theory from Shandong University, China in 2001, and received the Ph.D. degree in control theory and control engineering from Shanghai Jiaotong University, China in 2005. Currently she is a professor at the School of Mechatronic Engineering and Automation, Shanghai University, China.

Her research interests include scheduling theory and algorithm, robust discrete optimization theory and application, production planning and scheduling, and health-care management and optimization.

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Zhang, XX., Fu, ZQ., Li, SY. et al. A time/space separation based 3D fuzzy modeling approach for nonlinear spatially distributed systems. Int. J. Autom. Comput. 15, 52–65 (2018). https://doi.org/10.1007/s11633-017-1080-0

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  • DOI: https://doi.org/10.1007/s11633-017-1080-0

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