(299b) Hybrid Model-Based MPC with Guarantees on Stability and Applicability Domain: Application to Chemical, Biochemical, and Hydraulic Fracturing Systems

Process modeling began with the use of first-principles to build mathematical representations of complex chemical systems. These first-principles include mass and energy conservation laws, thermodynamic laws, kinetic laws, transport laws, etc. These first-principles-based models are interpretable and robust but have limited accuracy as they cannot explain all the complex phenomena that occur within a process [1]. On the other hand, data-based models are easy to build and accurate within their applicability domain (AD). But data-based models show poor accuracy outside the AD [2]. In order to overcome the limitations of both approaches, hybrid modeling is utilized which combines a first-principles-based model with a data-based model such that the resultant hybrid model is more accurate than the first-principles-based model. Recently, a hybrid model was developed for hydraulic fracturing system that utilized a deep neural network (DNN) as its data-based model [3]. One limitation of a DNN is that it shows poor extrapolation outside its AD. Consequently, a DNN-based hybrid model will inherit this limitation and will have poor accuracy outside its AD. Subsequently, the inability of the DNN-based hybrid model to extrapolate will gravely affect MPC performance and could also lead to instability issues. Therefore, it is critical to design an MPC controller with guarantees on stability as well as the AD with respect to the DNN-based hybrid model.

Recently, in the field of safety engineering, the concept of Control Barrier Function (CBF) was proposed which in combination with a Control Lyapunov Function (CLF) guarantees safety and stability for nonlinear systems. The proposed control method ensures the stability of the system without it entering the unsafe regions [4]. In this work, we propose to develop a Control Lyapunov-Barrier Function-based model predictive controller (CLBF-MPC) for solving the problem of guarantees on AD and stability of nonlinear systems. First, we build a DNN-based hybrid model for the nonlinear system, define its AD based on the training data, and theoretically, show that its generalization error is bounded within the AD. Second, a CLBF is calculated and then utilized to design an explicit control law which guarantees the convergence of the closed loop system to the steady state without venturing outside the AD. Next, a CLBF-MPC is developed which guarantees stability and avoidance of leaving the AD under sample-and-hold control implementation. Finally, we show the effectiveness of our approach through application to a continuous stirred tank reactor, bioreactor, and hydraulic fracturing systems.

Literature cited:

[1] Shah, P., Sheriff, M.Z., Bangi, M.S.F., Kravaris, C., Kwon, J.S.I., Botre, C., Hirota, J. Deep neural network-based hybrid modeling and experimental validation for an industry-scale fermentation process: Identification of time-varying dependencies among parameters. Chemical Engineering Journal, 135643, 2022.

[2] Alexandridis, A., Stogiannos, M., Papaioannou, N., Zois, E., Sarimveis, H. An inverse neural controller based on the applicability domain of RBF network models. Sensors, 18(1), 2018.

[3] Bangi, M.S.F., Kwon, J.S.I. Deep hybrid modeling of chemical process: application to hydraulic fracturing. Comput. Chem. Eng., 134:106696, 2020.

[4] Romdlonyab, M.Z., Jayawardhanaa, B. Stabilization with guaranteed safety using Control Lyapunov–Barrier Function. Automatica, 66:39-47, 2016.