  Connected and automated vehicles (CAVs) have a great potential to improve
traffic efficiency in mixed traffic systems, which has been demonstrated by
multiple numerical simulations and field experiments. However, some fundamental
properties of mixed traffic flow, including controllability and
stabilizability, have not been well understood. This paper analyzes the
controllability of mixed traffic systems and designs a system-level optimal
control strategy. Using the Popov-Belevitch-Hautus (PBH) criterion, we prove
for the first time that a ring-road mixed traffic system with one CAV and
multiple heterogeneous human-driven vehicles is not completely controllable,
but is stabilizable under a very mild condition. Then, we formulate the design
of a system-level control strategy for the CAV as a structured optimal control
problem, where the CAV's communication ability is explicitly considered.
Finally, we derive an upper bound for reachable traffic velocity via
controlling the CAV. Extensive numerical experiments verify the effectiveness
of our analytical results and the proposed control strategy. Our results
validate the possibility of utilizing CAVs as mobile actuators to smooth
traffic flow actively.
