  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.
