A Novel Data-Driven MPC Framework Using KDE and KPCA for Autonomous Vehicles

Modeling and controlling complex, nonlinear, large-scale systems such as autonomous vehicles presents significant challenges due to high dimensionality, uncertain dynamics, and real-time constraints. This paper introduces a novel data-driven predictive control framework that synergistically integrates Kernel Density Estimation (KDE), Kernel Principal Component Analysis (KPCA), and Hankel matrix representation to address these challenges. The Hankel matrix formulation captures temporal correlations in system dynamics, enabling an effective representation of state transitions and dynamic modes. This representation is complemented by KPCA for nonlinear dimensionality reduction and KDE for probabilistic uncertainty quantification, resulting in a comprehensive framework that maintains computational tractability without sacrificing model fidelity. We present a rigorous mathematical foundation for the integration of these techniques, establishing formal convergence guarantees and error bounds for the kernel-based approximations. The framework demonstrates remarkable efficiency in feature extraction, preserving 95% of system variance with only two principal components, while the KDE component provides robust probabilistic predictions essential for safe autonomous navigation. Extensive experimental validation on an autonomous vehicle platform yields outstanding performance metrics: lateral tracking errors of 0.0225 m (RMSE), heading errors of 0.0476 rad, and longitudinal velocity tracking errors of 0.2725 m/s. These results represent an 81.3-89.8% improvement over traditional MPC approaches across diverse operational scenarios, including urban navigation, highway driving, parking maneuvers, and obstacle avoidance. The computational efficiency of our approach (1.6 ms execution time) enables real-time implementation on standard automotive-grade embedded control units while maintaining 100% compliance with lateral safety constraints. Comprehensive comparative analysis against state-of-the-art methods demonstrates that our framework effectively addresses the fundamental challenges of nonlinearity, high dimensionality, uncertainty quantification, and real-time implementation in autonomous vehicle control. These contributions advance the field of data-driven control for complex, nonlinear, large-scale systems, offering a principled alternative to traditional model-based approaches with significant practical implications for autonomous driving technologies.