  The cooperative control of the connected and automated vehicle (CAV) is
recognized as an effective approach to alleviate traffic congestion and improve
traffic safety, especially for on-ramp bottlenecks. However, in the mixed
traffic, the uncertainty of human-driven vehicles (HDVs) makes the on-ramp
merging control for CAVs more challenging. This paper proposes a decentralized
optimal control method to address the merging control problem of CAVs at
highway on-ramps in the mixed traffic. We first formulate the optimal merging
control problem, which includes the constraints of safety and vehicle dynamics,
with the objectives of minimizing travel time and energy consumption. Then, a
control framework, combining control barrier functions (CBFs) and control
Lyapunov functions (CLFs) is proposed. CBFs render the system subject to
safety-critical constraints, while CLFs stabilize the system to the objectives.
In addition, to enable effective control of CAVs in the mixed traffic, a
recursive merging control framework is proposed, where HDVs are regarded as
disturbances, and CAVs collect surrounding vehicles' states repeatedly and
update their trajectories recursively to satisfy strict merging requirements.
Finally, the merging problem is reformulated as a quadratic programming
problem, which allows for real-time application. Simulation results show that
the proposed on-ramp merging control method is robust in resisting disturbance
from the HDV with traffic efficiency and energy economy improvement.
