(433g) Integrating Koopman Operator with Subspace Identification for Model Predictive Control (MPC) Design

Nonlinear dynamics are widely prevelent in chemical engineering processes, posing significant challenges in automatic control systems. There have been several nonlinear modeling algorithms to accurately model the dynamic behaviours of the processes for being used in nonlinear model predictive control (NMPC) frameworks, such as first-principles [1] and nonlinear data-driven approaches such artificial neural networks (ANN) [2]. The key challenge in these implementations is often the model identification. To address this issue, some researchers use approaches that represent the nonlinear dynamics in terms of linear terms, such as Koopman operator-based models [3]. The identification of a Koopman operator based on the first-principles model is challenging due to the complex dynamics of the system. In addition, first-principles models cannot be accessible easily in many practical situations. However, there have been several data-driven model identification methods developed to identify a linear model based on process historical data such as Subspace Identification (SID) and Dynamic Mode Decomposition (DMD) methods. DMD-based methods have been widely used to identify Koopman operators [3]. SID-based approaches, on the other hand, have not been integrated with the Koopman operator identification. Due to this and the fact that SID-based algorithms show reasonably good performance, we propose a novel modeling approach integrating SID with Koopman operator. In the first part, the superior performance of the SID-Koopman operator model is shown compared to DMD-Koopman operator. Next, the SID-Koopman operator model is utilized to implement MPC for an illustrative CSTR reactor. The efficacy of the proposed SID-Koopman-based MPC is shown using several set-point tracking scenarios for the CSTR example.

References

[1] Ganesh, H.S., Seo, K., Fritz, H. E., Edgar, T. F., Novoselac, A. and Baldea, M., 2021. Indoor air quality and energy management in buildings using combined moving horizon estimation and model predictive control. Journal of Building Engineering, 33, p.101552.

[2] Hassanpour, H., Corbett, B. and Mhaskar, P., 2020. Integrating dynamic neural network models with principal component analysis for adaptive model predictive control. Chemical Engineering Research and Design, 161, pp.26-37.

[3] Narasingam, A., Son, S. H. and Kwon, J. S. I., 2022. Data-driven feedback stabilisation of nonlinear systems: Koopman-based model predictive control. International Journal of Control, pp.1-12.