Statistical Machine Learning in Model Predictive Control of Nonlinear Processes

Zhe Wu, David Rincon, Quanquan Gu and Panagiotis D. Christofides
Additional contact information
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

Mathematics, 2021, vol. 9, issue 16, 1-37

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.

Keywords: generalization error; recurrent neural networks; machine learning; model predictive control; nonlinear systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/16/1912/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/16/1912/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:16:p:1912-:d:612751

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().