Sparse-identification-based model predictive control of nonlinear two-time-scale processes

This paper focuses on the design of model predictive controllers for nonlinear two-time-scale processes using only process measurement data. By first identifying and isolating the slow and fast variables in a two-time-scale process, the model predictive controller is designed based on the reduced slow subsystem consisting of only the slow variables, since the fast states can deteriorate controller performance when directly included in the model used in the controller. In contrast to earlier works, in the present work, the reduced slow subsystem is constructed from process data using sparse identification, which identifies nonlinear dynamical systems as first-order ordinary differential equations using an efficient, convex algorithm that is highly optimized and scalable. Results from the mathematical framework of singular perturbations are combined with standard assumptions to derive sufficient conditions for closed-loop stability of the full singularly perturbed closed-loop system. The effectiveness of the proposed controller design is illustrated via its application to a non-isothermal reactor with the concentration and temperature profiles evolving in different time-scales, where it is found that the controller based on the sparse identified slow subsystem can achieve superior closed-loop performance versus existing approaches for the same controller parameters.