  Connected automated vehicles (CAVs) could potentially be coordinated to
safely attain the maximum traffic flow on roadways under dynamic traffic
patterns, such as those engendered by the merger of two strings of vehicles due
a lane drop. Strings of vehicles have to be shaped correctly in terms of the
inter-vehicular time-gap and velocity to ensure that such operation is
feasible. However, controllers that can achieve such traffic shaping over the
multiple dimensions of target time-gap and velocity over a region of space are
unknown. The objective of this work is to design such a controller, and to show
that we can design candidate time-gap and velocity profiles such that it can
stabilize the string of vehicles in attaining the target profiles. Our analysis
is based on studying the system in the spacial rather than the time domain,
which enables us to study stability as in terms of minimizing errors from the
target profile and across vehicles as a function of location. Finally, we
conduct numeral simulations in the context of shaping two platoons for merger,
which we use to illustrate how to select time-gap and velocity profiles for
maximizing flow and maintaining safety.
