Data‐Driven Predictive Control for Nonlinear Systems: A Structured Prediction Approach With Kernelized Innovation Feedback

Abstract

Data‐driven predictive control (DDPC) methods have received increasing interest and gained exceptional success in linear systems. However, extending DDPC to nonlinear systems remains a challenging task, primarily due to the difficulty in balancing the complexity of the output predictor (OP) with generalization capability, and the inability of a static OP to cope with real‐time unmodeled dynamics. In this paper, we propose a novel nonlinear DDPC framework via a structured OP and a kernelized innovation‐based feedback mechanism. To effectively capture nonlinear dynamics from data, we first design a new structured predictor that consists of a nominal linear term for capturing coarse‐grained linear relations and a nonlinear term established in the reproducing kernel Hilbert space (RKHS), capturing fine‐grained nonlinearity. To further enhance robustness against unmodeled dynamics and disturbance, a kernelized feedback mechanism is designed to correct predicted outputs based on real‐time innovation sequences. A tailored heuristic algorithm based on alternating minimization is designed to effectively solve the data‐driven parameter estimation problem. By applying the data‐driven OP in the control regime, a new DDPC method for nonlinear systems is derived. Comprehensive studies on a nonlinear numerical example and a robotic manipulator demonstrate that the proposed method yields lower prediction errors and better tracking performance than the existing linear and nonlinear DDPC methods.