(594b) Online Data-Enabled Predictive Control Using Deep Learning

Complex industrial processes have been widely adopted across various industries to enhance operational safety, efficiency, and product. To obtain these advantages, it is important to employ effective advanced control strategies to regulate the process operation in real-time. Model predictive control (MPC) is one of the most widely recognized advanced control solutions [2,3]. The development of MPC typically requires an accurate dynamic model to characterize the process behaviors. However, with the increasing complexity of the industrial processes, it is challenging to derive a high-fidelity model for the underlying system. Alternatively, direct data-driven control has the potential to regulate the process using only data information without establishing a dynamic model [4].

In recent years, data-enabled predictive control (DeePC) has gained increasing attention as a promising direct data-driven control approach that relies solely on input and output data [5,6]. Based on Willems’ fundamental lemma [7], DeePC establishes a non-parametric representation of the system using a Hankel matrix constructed from historical input and output trajectories. However, the fundamental lemma is applicable only to linear time-invariant systems. For other types of systems, such as nonlinear systems, stochastic systems, and time-varying systems, the Hankel matrix may not adequately capture the system dynamics, which may result in poor control performance [8].

In the existing literature, several techniques and approaches have been proposed to address the limitations and enhance performance for the nonlinear systems and stochastic systems [5,9,10]. Furthermore, online DeePC approaches have been developed for time-varying systems [8,11,12]. In [11], an online updating approach for the Hankel matrix was proposed by replacing the old data with the most recent real-time input and output data. However, the persistently exciting condition of the fundamental lemma may not be satisfied. In [12], a recursive DeePC was proposed by continuously adding real-time input and output trajectories into the Hankel matrix. In [8], singular value decomposition was applied to select informative data during online implementation, and the Hankel matrix was updated by adding input and output trajectories discontinuously. However, continuously expanding the Hankel matrix without removing any data information can lead to significantly high computational complexity and pose challenges for solving the optimization problem during online implementation.

Based on the above observations, this study aims to integrate deep learning methods with DeePC to propose a computationally efficient updating approach for the Hankel matrix to better describe the varying dynamic behaviors of the system. By leveraging a deep neural network, we learn to extract features from input and output trajectories. During online implementation, the trained neural network captures the features from the most recent data and combines them with the preserved features obtained from the historical data and online data in the previous steps. The proposed approach is applied to a time-varying chemical process to evaluate its effectiveness.

References

[1] P. Daoutidis, J. H. Lee, I. Harjunkoski, S. Skogestad, M. Baldea, and C. Georgakis. Integrating operations and control: A perspective and roadmap for future research. Computers & Chemical Engineering, 115:179–184, 2018.
[2] M. Morari and L. J. Lee. Model predictive control: past, present and future. Computers & Chemical Engineering, 23(4-5):667–682, 1999.
[3] C. E. Garcia, D. M. Prett, and M. Morari. Model predictive control: Theory and practice—A survey. Automatica, 25(3):335–348, 1989.
[4] W. Tang and P. Daoutidis. Data-driven control: Overview and perspectives. American Control Conference, 1048–1064, 2022.
[5] J. Coulson, J. Lygeros, and F. Dörfler. Data-enabled predictive control: In the shallows of the DeePC. European Control Conference, 307–312, 2019.
[6] L. Huang, J. Zhen, J. Lygeros, and F. Dörfler. Robust data-enabled predictive control: Tractable formulations and performance guarantees. IEEE Transactions on Automatic Control, 68(5):3163–3170, 2023.
[7] J. C. Willems, P. Rapisarda, I. Markovsky, and B. L. De Moor. A note on persistency of excitation. Systems & Control Letters, 54(4):325–329, 2005.
[8] A. Vahidi-Moghaddam, K. Zhang, X. Yin, V. Srivastava, and Z. Li. Online reduced-order data-enabled predictive control. arXiv preprint arXiv:2407.16066, 2024.
[9] E. Elokda, J. Coulson, P. N. Beuchat, J. Lygeros, and F. Dörfler. Data-enabled predictive control for quadcopters. International Journal of Robust and Nonlinear Control, 31(18):8916–8936, 2021.
[10] J. Berberich, J. Köhler, M. A. Müller, and F. Allgöwer. Data-driven model predictive control: closed-loop guarantees and experimental results. at-Automatisierungstechnik, 69(7):608–618, 2021.
[11] S. Baros, C. Y. Chang, G. E. Colon-Reyes, and A. Bernstein. Online data-enabled predictive control. Automatica, 138:109926, 2022.
[12] J. Shi and C. N. Jones. Efficient recursive data-enabled predictive control: an application to consistent predictors. arXiv preprint arXiv:2309.13755, 2023.