Direct Data-Driven Trajectory Tracking Control for Autonomous Vehicles via Algebraic Regulator Under Limited Data

In autonomous vehicle trajectory tracking, the absence of an accurate vehicle dynamics model can significantly degrade tracking performance. While model-free approaches, such as neural network-based supervised learning and deep reinforcement learning, have shown promising results, they typically require large-scale datasets and long-term training to ensure control convergence and generalizability. To overcome these challenges, we propose the direct data-driven trajectory tracking algebraic regulator, a model-free control framework designed to achieve high-precision trajectory tracking under limited data availability. The tracking problem is first reformulated as an output regulation problem involving an unknown plant and a predefined reference system. Then, leveraging a finite set of input–state data with representative reference trajectories, we synthesize a data-driven feedback control law using an algebraic regulator and semidefinite programming, accounting for both noise-free and noisy datasets. In addition, we formally derive the minimal data required to guarantee the solvability of the regulator, providing practical guidance for data collection. More importantly, we present rigorous theoretical analyses establishing exponential stability of the closed-loop system in the noise-free data setting and exponential convergence to a bounded error in the presence of noisy data. The convergence rate is also thoroughly examined and explicitly characterized. Finally, the effectiveness of the proposed approach is validated through a hardware-in-the-loop experimental setup based on a CarSim/dSPACE platform, demonstrating superior tracking performance compared with benchmark methods, including PID, Stanley, model predictive control, and data-enabled predictive control.