Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Machine Learning-Based Model Predictive Control of Two-Time-Scale Systems

Journal Article · · Mathematics
DOI:https://doi.org/10.3390/math11183827· OSTI ID:2418521
 [1];  [2];  [2];  [2]
  1. Univ. of California, Los Angeles, CA (United States); Univ. of California, Los Angeles, CA (United States)
  2. Univ. of California, Los Angeles, CA (United States)
+ Show Author Affiliations

In this study, we present a general form of nonlinear two-time-scale systems, where singular perturbation analysis is used to separate the dynamics of the slow and fast subsystems. Machine learning techniques are utilized to approximate the dynamics of both subsystems. Specifically, a recurrent neural network (RNN) and a feedforward neural network (FNN) are used to predict the slow and fast state vectors, respectively. Moreover, we investigate the generalization error bounds for these machine learning models approximating the dynamics of two-time-scale systems. Next, under the assumption that the fast states are asymptotically stable, our focus shifts toward designing a Lyapunov-based model predictive control (LMPC) scheme that exclusively employs the RNN to predict the dynamics of the slow states. Additionally, we derive sufficient conditions to guarantee the closed-loop stability of the system under the sample-and-hold implementation of the controller. A nonlinear chemical process example is used to demonstrate the theory. In particular, two RNN models are constructed: one to model the full two-time-scale system and the other to predict solely the slow state vector. Both models are integrated within the LMPC scheme, and we compare their closed-loop performance while assessing the computational time required to execute the LMPC optimization problem.

Research Organization:
Univ. of California, Los Angeles, CA (United States)
Sponsoring Organization:
USDOE Office of Energy Efficiency and Renewable Energy (EERE), Energy Efficiency Office. Advanced Manufacturing Office; National Science Foundation (NSF)
Grant/Contract Number:
EE0007613
OSTI ID:
2418521
Journal Information:
Mathematics, Journal Name: Mathematics Journal Issue: 18 Vol. 11; ISSN 2227-7390
Publisher:
MDPICopyright Statement
Country of Publication:
United States
Language:
English

References (17)

Composite fast-slow MPC design for nonlinear singularly perturbed systems journal April 2012
Machine‐learning‐based predictive control of nonlinear processes. Part II: Computational implementation journal July 2019
Properties of solutions of ordinary differential equations with small parameters journal November 1971
Learning‐based adaptive‐scenario‐tree model predictive control with improved probabilistic safety using robust Bayesian neural networks journal December 2022
On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming journal April 2005
Experiment study of machine-learning-based approximate model predictive control for energy-efficient building control journal April 2021
On generalization error of neural network models and its application to predictive control of nonlinear processes journal January 2023
Sparse-identification-based model predictive control of nonlinear two-time-scale processes journal October 2021
Statistical machine-learning-based predictive control using barrier functions for process operational safety journal July 2022
Polynomial NARX-based nonlinear model predictive control of modular chemical systems journal September 2023
Economic model predictive control of nonlinear singularly perturbed systems journal June 2013
A learning- and scenario-based MPC design for nonlinear systems in LPV framework with safety and stability guarantees journal May 2023
Feedback control of two-time-scale nonlinear systems journal March 1996
Singular perturbations and input-to-state stability journal January 1996
Long Short-Term Memory journal November 1997
Approximating Explicit Model Predictive Control Using Constrained Neural Networks conference June 2018
Statistical Machine Learning in Model Predictive Control of Nonlinear Processes journal August 2021

Figures / Tables (12)

Figure 1(p. 8)figure Figure 1
Figure 2(p. 9)figure Figure 2
Figure 3(p. 22)figure Figure 3
Table 1(p. 23)table Table 1
Table 2(p. 25)table Table 2
Figure 4(p. 27)figure Figure 4
Table 3(p. 27)table Table 3
Figure 5(p. 28)figure Figure 5
Figure 6(p. 28)figure Figure 6
Figure 7(p. 29)figure Figure 7
Figure 8(p. 29)figure Figure 8
Figure 9(p. 30)figure Figure 9

Similar Records

Machine‐learning‐based predictive control of nonlinear processes. Part II: Computational implementation
Journal Article · Wed Jul 31 00:00:00 EDT 2019 · AIChE Journal · OSTI ID:1545905
Machine‐learning‐based construction of barrier functions and models for safe model predictive control
Journal Article · Wed Oct 06 00:00:00 EDT 2021 · AIChE Journal · OSTI ID:1824904
Dynamic process modeling with recurrent neural networks
Journal Article · Fri Oct 01 00:00:00 EDT 1993 · AIChE Journal (American Institute of Chemical Engineers); (United States) · OSTI ID:5996396

Related Subjects

97 MATHEMATICS AND COMPUTING
feedforward neural network
long short-term memory recurrent neural networks
machine learning
model predictive control
nonlinear systems
process control
recurrent neural networks
singular perturbations
two-time-scale systems