Statistical machine‐learning–based predictive control of uncertain nonlinear processes

• Published in: AIChE journal Vol. 68; no. 5
• Main Authors: Wu, Zhe, Alnajdi, Aisha, Gu, Quanquan, Christofides, Panagiotis D.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.05.2022; American Institute of Chemical Engineers
• Subjects: Chemical reactors; Disturbances; generalization error; Learning algorithms; Learning theory; Machine learning; model predictive control; Neural networks; Nonlinear control; Nonlinear systems; Predictive control; Recurrent neural networks; Statistical prediction; Statistics; stochastic nonlinear systems; Systems stability
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.17642

In this study, we present machine‐learning–based predictive control schemes for nonlinear processes subject to disturbances, and establish closed‐loop system stability properties using statistical machine learning theory. Specifically, we derive a generalization error bound via Rademacher complexity method for the recurrent neural networks (RNN) that are developed to capture the dynamics of the nominal system. Then, the RNN models are incorporated in Lyapunov‐based model predictive controllers, under which we study closed‐loop stability properties for the nonlinear systems subject to two types of disturbances: bounded disturbances and stochastic disturbances with unbounded variation. A chemical reactor example is used to demonstrate the implementation and evaluate the performance of the proposed approach.