(434a) Physics-Based Machine Learning Modeling for Model Predictive Control of Nonlinear Processes

While recurrent neural networks (RNN), a class of artificial neural networks that can represent temporal dynamic behavior through feedback loops in neurons, have been widely-used used to model nonlinear dynamic systems based on process operating data [1, 2], they are generally treated as a black-box modeling approach where no physical knowledge is utilized in determing the RNN structure and parameters, and therefore, interpretability and optimality of neural network modeling remain in general questionable. On the other hand, chemical processes have been studied for a long time by researchers and engineers, where first-principles knowledge has been obtained based on their predefined and well-known structure. Therefore, how to efficiently incorporate first-principles and physical knowledge of chemical processes into RNN modeling is an important research issue [3, 4, 5].

In this work, we propose three modeling approaches: a hybrid model, a partially-connected RNN model, and a weight-constrained RNN model, to incorporate process physical knowledge into RNN modeling and training. The proposed physics-based RNN models that are developed for a general class of input-constrained nonlinear processes are then incorporated in the design of model predictive control (MPC) systems and of economic MPC (EMPC) systems to optimize process performance in terms of closed-loop stability and economic optimality, respectively. Through the application to an illustrative chemical process example, we demonstrate that improved closed-loop performances in terms of faster convergence to the steady-state under RNN-MPC and enhanced process economic profits under RNN-EMPC are achieved compared to the controllers using black-box (i.e., process structure unaware) RNN models.

[1] Kosmatopoulos, E. B., Polycarpou, M. M., Christodoulou, M. A., and Ioannou, P. A. High-order neural network structures for identification of dynamical systems. IEEE transactions on Neural Networks, 6, 422-431, 1995

[2] Wu, Z., A. Tran, D. Rincon and P. D. Christofides, "Machine Learning-Based Predictive Control of Nonlinear Processes. Part I: Theory,'' AIChE J., 65, e16729, 2019.

[3] D.C. Psichogios and L.H. Ungar. A hybrid neural network-first principles approach to process modeling. AIChE Journal, 38:1499–1511, 1992.

[4] A. Karpatne, W. Watkins, J. Read, and V. Kumar. Physics-guided neural networks (PGNN): An application in lake temperature modeling. arXiv preprint arXiv:1710.11431, 2017

[5] Y. Lu, M. Rajora, P. Zou, and S. Liang. Physics-embedded machine learning: case study with electrochemical micro-machining. Machines, 5:4, 2017.