Machine learning-based predictive control of nonlinear time-delay systems - Closed-loop stability and input delay compensation - academic research

Aug 5, 2026

This work develops machine-learning-based model predictive control for nonlinear systems affected by time delays. An LSTM model is first trained to learn process dynamics when delays are absent, and the resulting LSTM-based MPC is used to stabilize the delay-free nonlinear system with demonstrated closed-loop stability. The study further extends the controller to handle input delays by introducing an LSTM-based predictor that compensates delay effects and initializes the MPC with predicted future states. The method is evaluated on a chemical process example using simulations to assess performance and robustness.

LanguageEnglish

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Introduction

Machine learning for nonlinear process control

LSTM networks and MPC background

UCLA UCLA Previously Published Works Title Machine learning-based predictive control of nonlinear time-delay systems: Closed-loop stability and input delay compensation Permalink [https://escholarship.org/uc/item/0zr2w57q](https://escholarship.org/uc/item/0zr2w57q) Authors Alnajdi, Aisha Suryavanshi, Atharva Alhajeri, Mohammed Set al. Publication Date 2023-06-01 DOI 10.1016/j.dche.2023.100084 Peer reviewed [eScholarship.org](eScholarship.org) Powered by the California Digital Library University of California Digital Chemical Engineering 7 (2023) 100084 | Best practices and methods
Machine learning-based predictive control of nonlinear time-delay systems: Closed-loop stability and input delay compensation
Aisha Alnajdia,d, Atharva Suryavanshi b, Mohammed S. Alhajerib,c, Fahim Abdullah b, Panagiotis D. Christofides a,b,∗
a Department of Electrical and Computer Engineering, University of California, Los Angeles, CA 90095 -1592, USA b Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA, 90095 -1592, USAc Department of Chemical Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait
d Department of Electrical Engineering, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait | | | | | --- | --- | --- | --- | | A R T I C L E I N F O | | A B S T R A C T | | | Keywords:
Nonlinear time-delay systems Recurrent neural networks Long short-term memory Machine learning
Process control
Model predictive control Nonlinear systems | | The purpose of this work is to study machine-learning-based model predictive control of nonlinear systems with time-delays. The proposed approach involves initially building a machine learning model (i.e., Long Short Term Memory (LSTM)) to capture the process dynamics in the absence of time delays. Then, an LSTM-based model predictive controller (MPC) is designed to stabilize the nonlinear system without time delays. Closed-loop stability results are then presented, establishing robustness of this LSTM-based MPC towards small time-delaysin the states. To handle input delays, we design an LSTM-based MPC with an LSTM-based predictor that compensates for the effect of input delays. The predictor is used to predict future states using the process measurement, and then the predicted states are used to initialize the LSTM-based MPC. Stabilization of the time-delay system with both state and input delays around the steady state is achieved through the featured design. The approach is applied to a chemical process example, and its performance and robustness properties are evaluated via simulations. | | 1. Introduction Machine learning algorithms have generated considerable interest in the field of control of nonlinear process systems. This is because of their ability to capture the system’s dynamics and to model largescale, complex, nonlinear systems. Moreover, the existence of large data sets, powerful computers, and the variety of machine learning training algorithms have contributed to the recent surge of machine learning being applied to numerous engineering applications. Although, historically, first-principles modeling approaches have been widely adapted in modeling chemical processes, they can be difficult and/or time-consuming to derive when dealing with large-scale, complex, nonlinear processes. In contrast, machine learning techniques have made a significant impact in the field of nonlinear control systems and have shown great success in modeling large-scale, complex, nonlinear processes (e.g., Wu et al. (2019a,b), Chen et al. (2012, 2020), Alhajeriet al. (2021), Wu et al. (2021a,b, 2022)). Researchers in the field have started adapting the science of machine learning since the 90’s (Hoskins and Himmelblau, 1992; Vepa, 1993), when they started introducing the concept of machine learning to the field of chemical engineering, and many promising contributions and applications have been observed s

FAQs

What is the main goal of the proposed control method?

To design an LSTM-based model predictive controller for nonlinear systems with time delays, including both closed-loop stabilization and compensation of input-delay effects.

How is the LSTM model used in the controller design?

An LSTM model is first trained to capture process dynamics without delays, and then an LSTM-based MPC uses this learned model to stabilize the nonlinear system.

How does the method compensate for input delays?

It introduces an LSTM-based predictor that compensates the effect of input delays, predicts future states from measurements, and uses those predictions to initialize the LSTM-based MPC.

Aug 5, 2026

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