  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.
