IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1912-d612751.html
   My bibliography  Save this article

Statistical Machine Learning in Model Predictive Control of Nonlinear Processes

Author

Listed:
  • Zhe Wu

    (Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095-1592, USA)

  • David Rincon

    (Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095-1592, USA)

  • Quanquan Gu

    (Department of Computer Science, University of California, Los Angeles, CA 90095-1592, USA)

  • Panagiotis D. Christofides

    (Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095-1592, USA
    Department of Electrical and Computer Engineering, University of California, Los Angeles, CA 90095-1592, USA)

Abstract

Recurrent neural networks (RNNs) have been widely used to model nonlinear dynamic systems using time-series data. While the training error of neural networks can be rendered sufficiently small in many cases, there is a lack of a general framework to guide construction and determine the generalization accuracy of RNN models to be used in model predictive control systems. In this work, we employ statistical machine learning theory to develop a methodological framework of generalization error bounds for RNNs. The RNN models are then utilized to predict state evolution in model predictive controllers (MPC), under which closed-loop stability is established in a probabilistic manner. A nonlinear chemical process example is used to investigate the impact of training sample size, RNN depth, width, and input time length on the generalization error, along with the analyses of probabilistic closed-loop stability through the closed-loop simulations under Lyapunov-based MPC.

Suggested Citation

  • Zhe Wu & David Rincon & Quanquan Gu & Panagiotis D. Christofides, 2021. "Statistical Machine Learning in Model Predictive Control of Nonlinear Processes," Mathematics, MDPI, vol. 9(16), pages 1-37, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1912-:d:612751
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1912/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1912/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Constantin Volosencu, 2022. "Study of the Angular Positioning of a Rotating Object Based on Some Computational Intelligence Methods," Mathematics, MDPI, vol. 10(7), pages 1-46, April.
    2. Aisha Alnajdi & Fahim Abdullah & Atharva Suryavanshi & Panagiotis D. Christofides, 2023. "Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems," Mathematics, MDPI, vol. 11(18), pages 1-31, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1912-:d:612751. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.