The positive impacts of platooning on travel time reliability, congestion, emissions, and energy consumption have been shown for homogeneous roadway segments. However, speed limit changes frequently throughout the transportation network, due to either safety-related considerations (e.g., workzone operations) or congestion management schemes (e.g., speed harmonization systems). These abrupt changes in speed limit can result in shock- wave formation and cause travel time unreliability. Therefore, designing a platooning strategy for tracking a reference velocity profile is critical to enabling end-to-end platooning. Accordingly, this study introduces a generalized control model to track a desired velocity profile, while ensuring safety in the platoon of autonomous vehicles. We define appropriate natural error terms and the target curve in the state space of the control system, which is the set of points where all error terms vanish and corresponds to the case when all vehicles move with the desired velocities and in the minimum safe distance between them. In this way, we change the tracking velocity profile problem into a state- feedback stabilization problem with respect to the target curve. Under certain mild assumptions on the Lipschitz constant of the speed drop profile, we show that the stabilizing feedback can be obtained via introducing a natural dynamics for the maximum of the error terms for each vehicle. Moreover, we show that with this stabilizing feedback collisions will not occur if the initial state of the system of vehicles is sufficiently close to the target curve. We also show that the error terms remain bounded throughout the time and space. Two scenarios were simulated, with and without initial perturbations, and results confirmed the effectiveness of the proposed control model in tracking the speed drop while ensuring safety and string stability.
