Data-Driven Linear Parameter-Varying Model Predictive Control for Unknown Nonlinear Systems

This article proposes a data-driven linear parameter variation model predictive control (DDLPVMPC) method for unknown nonlinear (NL) systems. The approach eliminates reliance on prior knowledge by autonomously constructing system models directly from data. Specifically, a sparse regression-based method is developed to automatically identify the optimal scheduling variables, enabling high-precision LPV approximation of complex system dynamics. Secondly, an innovative error compensation mechanism is introduced to dynamically incorporate the modeling residuals into the scheduling variables, which further improves the model accuracy and disturbance-resistant capability. Furthermore, the LPV-model predictive controller is efficiently realized by embedding the LPV model into the model predictive control (MPC) optimization problem using a local approximation strategy, which enables real-time control of NL systems with constrained inputs. Numerical simulations and robotic manipulator trajectory tracking experiments show that DDLPVMPC is superior to the existing representative methods in terms of modeling accuracy and control performance.