  The emergence of autonomous vehicles is expected to revolutionize road
transportation in the near future. Although large-scale numerical simulations
and small-scale experiments have shown promising results, a comprehensive
theoretical understanding to smooth traffic flow via autonomous vehicles is
lacking. In this paper, from a control-theoretic perspective, we establish
analytical results on the controllability, stabilizability, and reachability of
a mixed traffic system consisting of human-driven vehicles and autonomous
vehicles in a ring road. We show that the mixed traffic system is not
completely controllable, but is stabilizable, indicating that autonomous
vehicles can not only suppress unstable traffic waves but also guide the
traffic flow to a higher speed. Accordingly, we establish the maximum traffic
speed achievable via controlling autonomous vehicles. Numerical results show
that the traffic speed can be increased by over 6% when there are only 5%
autonomous vehicles. We also design an optimal control strategy for autonomous
vehicles to actively dampen undesirable perturbations. These theoretical
findings validate the high potential of autonomous vehicles to smooth traffic
flow.
