This paper introduces an online physical enhanced residual learning (PERL) framework for Connected Autonomous Vehicles (CAVs) platoon, aimed at addressing the challenges posed by the dynamic and unpredictable nature of traffic environments. The proposed framework synergistically combines a physical model, represented by Model Predictive Control (MPC), with data-driven online Q-learning. The MPC controller, enhanced for centralized CAV platoons, employs vehicle velocity as a control input and focuses on multi-objective cooperative optimization. The learning-based residual controller enriches the MPC with prior knowledge and corrects residuals caused by traffic disturbances. The PERL framework not only retains the interpretability and transparency of physics-based models but also significantly improves computational efficiency and control accuracy in real-world scenarios. The experimental results present that the online Q-learning PERL controller, in comparison to the MPC controller and PERL controller with a neural network, exhibits significantly reduced position and velocity errors. Specifically, the PERL's cumulative absolute position and velocity errors are, on average, 86.73% and 55.28% lower than the MPC's, and 12.82% and 18.83% lower than the neural network-based PERL's, in four tests with different reference trajectories and errors. The results demonstrate our advanced framework's superior accuracy and quick convergence capabilities, proving its effectiveness in maintaining platoon stability under diverse conditions.
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