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

Aisha Alnajdi, Fahim Abdullah, Atharva Suryavanshi and Panagiotis D. Christofides ()
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Aisha Alnajdi: Department of Electrical and Computer Engineering, University of California, Los Angeles, CA 90095, USA
Fahim Abdullah: Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095, USA
Atharva Suryavanshi: Department of Chemical and Biomolecular Engineering, University of California, Los Angeles, CA 90095, USA
Panagiotis D. Christofides: Department of Electrical and Computer Engineering, University of California, Los Angeles, CA 90095, USA

Mathematics, 2023, vol. 11, issue 18, 1-31

Abstract: 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.

Keywords: two-time-scale systems; machine learning; recurrent neural networks; long short-term memory recurrent neural networks; feedforward neural network; process control; model predictive control; nonlinear systems; singular perturbations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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