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Model-based predictive control for spatially-distributed systems using dimensional reduction models

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Abstract

In this paper, a low-dimensional multiple-input and multiple-output (MIMO) model predictive control (MPC) configuration is presented for partial differential equation (PDE) unknown spatially-distributed systems (SDSs). First, the dimension reduction with principal component analysis (PCA) is used to transform the high-dimensional spatio-temporal data into a low-dimensional time domain. The MPC strategy is proposed based on the online correction low-dimensional models, where the state of the system at a previous time is used to correct the output of low-dimensional models. Sufficient conditions for closed-loop stability are presented and proven. Simulations demonstrate the accuracy and efficiency of the proposed methodologies.

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Authors and Affiliations

  1. Institute of Automation, Shanghai Jiao Tong University, Shanghai, 200240, PRC

    Meng-Ling Wang, Ning Li & Shao-Yuan Li

  2. Key Laboratory of System Control and Information Processing, Ministry of Education, Shanghai, 200240, PRC

    Meng-Ling Wang, Ning Li & Shao-Yuan Li

Authors
  1. Meng-Ling Wang
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  2. Ning Li
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  3. Shao-Yuan Li
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Corresponding author

Correspondence to Shao-Yuan Li.

Additional information

This work was supported by National High Technology Research and Development Program of China (863 Program) (No. 2009AA04Z162), National Nature Science Foundation of China (No. 60825302, No. 60934007, No. 61074061), Program of Shanghai Subject Chief Scientist, “Shu Guang” project supported by Shanghai Municipal Education Commission and Shanghai Education Development Foundation, and Key Project of Shanghai Science and Technology Commission, China (No. 10JC1403400).

Meng-Ling Wang graduated from Jiangsu Polytechnic University, PRC in 2002. She received the M. Sc. degree from East China University of Science and Technology, PRC in 2005. She is currently a Ph.D. candidate in the Institute of Automation, Shanghai Jiao Tong University, PRC.

Her research interests include intelligent computing and predictive control.

Ning Li graduated from Qingdao University of Science and Technology, PRC in 1996. She received the M. Sc. degrees from Qingdao University of Science and Technology in 1999, and the Ph.D. degree from Shanghai Jiao Tong University, PRC in 2002. She is currently an associate professor of the Institute of Automation, Shanghai Jiao Tong University.

Her research interests include modeling and control of complex systems and fuzzy systems.

Shao-Yuan Li graduated from Hebei University of Technology, PRC in 1987. He received the M. Sc. degrees from Hebei University of Technology, PRC in 1992, and Ph.D. degree from Nankai University, PRC in 1997. He is currently a professor of the Institute of Automation, Shanghai Jiao Tong University, PRC.

His research interests include nonlinear system control and fuzzy systems.

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Wang, ML., Li, N. & Li, SY. Model-based predictive control for spatially-distributed systems using dimensional reduction models. Int. J. Autom. Comput. 8, 1–7 (2011). https://doi.org/10.1007/s11633-010-0547-z

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  • DOI: https://doi.org/10.1007/s11633-010-0547-z

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