Machine learning modeling and predictive control of nonlinear processes using noisy data

This work focuses on machine learning modeling and predictive control of nonlinear processes using noisy data. We use long short-term memory (LSTM) networks with training data from sensor measurements corrupted by two types of noise: Gaussian and non-Gaussian noise, to train the process model that will be used in a model predictive controller (MPC). We first discuss the LSTM training with noisy data following a Gaussian distribution, and demonstrate that the standard LSTM network is capable of capturing the underlying process dynamic behavior by reducing the impact of noise. Subsequently, given that the standard LSTM performs poorly on a noisy data set from industrial operation (i.e., non-Gaussian noisy data), we propose an LSTM network using Monte Carlo dropout method to reduce the overfitting to noisy data. Furthermore, an LSTM network using co-teaching training method is proposed to further improve its approximation performance when noise-free data from a process model capturing the nominal process state evolution is available. A chemical process example is used throughout the manuscript to illustrate the application of the proposed modeling approaches and demonstrate their open- and closed-loop performance under a Lyapunov-based model predictive controller with state measurements corrupted by industrial noise.