  We consider an asymmetric control of platoons of identical vehicles with
nearest-neighbor interaction. Recent results show that if the vehicle uses
different asymmetries for position and velocity errors, the platoon has a short
transient and low overshoots. In this paper we investigate the properties of
vehicles with friction. To achieve consensus, an integral part is added to the
controller, making the vehicle a third-order system. We show that the
parameters can be chosen so that the platoon behaves as a wave equation with
different wave velocities. Simulations suggest that our system has a better
performance than other nearest-neighbor scenarios. Moreover, an
optimization-based procedure is used to find the controller properties.
