Data-Driven Robust MPC for Unknown Nonlinear Systems via Set-Membership Learning

Abstract

Data-driven model predictive control (MPC) has become an attractive approach for controlling unknown systems, especially when data are corrupted by noise. However, most existing data-driven MPC methods focus on linear systems, and little attention has been given to nonlinear dynamics under disturbances. To fill this gap, we propose a robust data-driven min-max MPC scheme for unknown nonlinear systems with process disturbances. We represent the unknown nonlinear dynamics using vector fields built from a dictionary of basis functions, yielding an equivalent linear form with unknown matrices. These unknown matrices are characterized by a set-membership representation derived from noisy input-state data. Using this uncertainty description, we formulate a min-max MPC problem. Two online scenarios are studied: i) when state measurements are noise-free, and, ii) when they are corrupted by process disturbance. For each case, we derive a Lyapunov-based semidefinite program (SDP) to compute a stabilizing state-feedback controller. The resulting schemes are shown to guarantee recursive feasibility and either exponential or robust stability of the closed-loop system depending on whether there is process disturbance. Simulation studies on benchmark examples illustrate the effectiveness and competitive performance of the proposed approach compared to existing data-driven and model-based controllers.