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An Adaptive Model Predictive Control Strategy for Nonlinear Distributed Parameter Systems using the Type-2 Takagi–Sugeno Model

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Abstract

This paper proposes an adaptive model predictive control (MPC) strategy for nonlinear distributed parameter systems (DPSs) based on the online-tuning interval Type-2 Takagi-Sugeno (IT2 T–S) model. First, the infinite dimension DPS is approximated in a finite dimensional space via the finite difference method, and from this model, training data are generated. Principal component analysis is then used to project the finite, but still high, dimensional spatiotemporal training data into a low-dimensional time series using spatial basis functions. Next, an online-tuning IT2 T–S fuzzy model is proposed to predict the low-dimensional time series with a high accuracy by computing an optimal time-varying weight parameter. Furthermore, a new method for simplifying controller design is presented by transforming the control objective from the high-dimensional spatial outputs reaching their set points to the lower dimensional time outputs reaching their set points. These novel contributions increase the accuracy of the prediction model (thus improving control performance) and reduce the computational cost of the underlying MPC optimization. Lastly, simulations are presented on a typical DPS to demonstrate the accuracy and effectiveness of the proposed methods.

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Acknowledgments

This work was supported by the National Nature Science Foundation of China (No. 61203059, No. 61272064, and No. 61374140), the Fundamental Research Funds for the Central Universities (No. 22A201514048), and the Open Research fund for Key Laboratory of Embedded System and Service Computing, Ministry of Education, Tongji University.

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Authors and Affiliations

  1. Key Laboratory of Advanced Control and Optimization for Chemical Processes of Ministry of Education, East China University of Science and Technology, 130, Meilong Road, Shanghai, 200237, China

    Mengling Wang, Huaicheng Yan & Hongbo Shi

  2. Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    Joel A. Paulson

Authors
  1. Mengling Wang
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  2. Joel A. Paulson
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  3. Huaicheng Yan
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  4. Hongbo Shi
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Correspondence to Mengling Wang.

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Wang, M., Paulson, J.A., Yan, H. et al. An Adaptive Model Predictive Control Strategy for Nonlinear Distributed Parameter Systems using the Type-2 Takagi–Sugeno Model. Int. J. Fuzzy Syst. 18, 792–805 (2016). https://doi.org/10.1007/s40815-015-0115-3

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