Data-Driven Linear Predictive Control of Nonlinear Processes Based on Reduced-Order Koopman Operator

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state space into a higher-dimensional linear function space, in which Koopman-based linear models may be constructed for the underlying nonlinear process. To address the potential issue of a significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the proposed framework.