(543h) On-Line Learning in Model Predictive Control of Nonlinear Processes: Generalization Guarantees and Stability Analysis

Recurrent neural networks (RNN) have shown promising potential for modeling complex nonlinear processes in model predictive control (MPC) due to their ability to capture nonlinear dynamics utilizing time-series data. However, since neural network models are generally trained offline using the past data from normal operations (without model uncertainty) while the actual process model may vary over time in the presence of model uncertainty, the offline-trained RNN model cannot accurately predict real-time process dynamics, which remains a fundamental issue that limits the application of the machine-learning-based MPC to industrial chemical processes. To address this issue, on-line learning of machine learning (ML) models has been utilized in MPC to update the ML models in real time as more training data is collected [1, 2]. Additionally, to evaluate the generalization performance of RNN models and closed-loop stability properties of RNN-based MPC, a generalization error bound for offline-trained RNN models has been developed via statistical ML theory, and incorporated in MPC to derive probabilistic closed-loop stability [3]. However, at this stage, the generalization performance for online learning of RNN models within MPC has not been studied.

Motivated by the above considerations, in this work, we will take advantage of statistical learning theory [4] and on-line learning approach [5] to develop generalization guarantees and closed-loop stability analysis for real-time machine-learning-based MPC of nonlinear processes in the presence of model uncertainty. Specifically, an ensemble of RNN models will be initially developed off-line to model process dynamics under normal operations. Subsequently, an on-line learning of RNN models will be carried out using real-time process data with learning guarantees for the updated ensemble of RNNs using the notion of regret, which can be viewed as a general methodology to measure the generalization performance of the updated RNN models. Based on the RNN learning guarantees, we will further investigate the closed-loop stability properties for the nonlinear processes under RNN-based MPC. Finally, the proposed on-line learning methodology will be applied to a nonlinear chemical process to demonstrate its effectiveness.

[1] Wu, Z., Rincon, D. and Christofides, P. D., (2019). Real-time adaptive machine-learning-based predictive control of nonlinear processes. Industrial & Engineering Chemistry Research, 59(6), pp.2275-2290.

[2] Maiworm, M., Limon, D., & Findeisen, R. (2021). Online learning‐based model predictive control with Gaussian process models and stability guarantees. International Journal of Robust and Nonlinear Control, 31(18), 8785-8812.

[3] Wu, Z., Rincon, D., Gu, Q. and Christofides, P. D., (2021). Statistical Machine Learning in Model Predictive Control of Nonlinear Processes. Mathematics, 9(16), p.1912.

[4] Mohri, M., Rostamizadeh, A. and Talwalkar, A., (2018). Foundations of machine learning. MIT press.

[5] Kuznetsov, V. and Mohri, M., (2016). Time series prediction and online learning. In Conference on Learning Theory (pp. 1190-1213). PMLR.