A Kernelized Operator Approach to Nonlinear Data-Enabled Predictive Control

Abstract: This paper considers the design of nonlinear data-enabled predictive control (DeePC) using kernel functions. Compared with existing methods that use kernels to parameterize multi-step predictors for nonlinear DeePC, we adopt a novel, operator-based approach. More specifically, we employ a universal product kernel parameterization of nonlinear systems operators as a prediction mechanism for nonlinear DeePC. We show that by using a product reproducing kernel Hilbert space (RKHS) to learn the system trajectories, big data sets can be handled effectively to construct the corresponding product Gram matrix. Moreover, we show that the structure of the adopted product RKHS representation allows for a computationally efficient DeePC formulation. Compared to existing methods, our approach achieves substantially faster computation times for the same data size. This allows for the use of much larger data sets and enhanced control performance.