Model predictive control of nonlinear processes using neural ordinary differential equation models

Abstract

Neural Ordinary Differential Equation (NODE) is a recently proposed family of deep learning models that can perform a continuous approximation of a linear/nonlinear dynamic system using time-series data by integrating the neural network model with classical ordinary differential equation solvers. Modeling nonlinear dynamic processes using data has historically been a critical challenge in the field of chemical engineering research. With the development of computer science and neural network technology, recurrent neural networks (RNN) have become a popular black-box approach to accomplish this task and have been utilized to design model predictive control (MPC) systems. However, as a discrete-time approximation model, RNN requires strictly uniform step sequence data to operate, which makes it less robust to an irregular sampling scenario, such as missing data points during operation due to sensor failure or other types of random errors. This paper aims to develop a NODE model and construct an MPC based on this novel continuous-time neural network model. In this context, closed-loop stability is established and robustness to noise is addressed using a variety of data analysis techniques. An example of a chemical process is utilized to evaluate the performance of NODE-based MPC. Furthermore, the performance of the NODE-based MPC under Gaussian and non-Gaussian noise is investigated, and the subsampling method is found to be effective in building models for MPC that are suitable for handling the presence of non-Gaussian noise in the data.