  This contribution introduces a centralized input constrained optimal control
framework based on multiple control barrier functions (CBFs) to coordinate
connected and automated agents at intersections. For collision avoidance, we
propose a novel CBF which is safe by construction. The given control scheme
provides provable guarantees that collision avoidance CBFs and CBFs to
constrain the agents' velocity are jointly feasible (referred to as
control-sharing property) subject to input constraints. A simulation study
finally provides evidence that the proposed control scheme is safe.
