  Connected and automated vehicles (CAVs) provide the most intriguing
opportunity to improve energy efficiency, traffic flow, and safety. In earlier
work, we addressed the constrained optimal coordination problem of CAVs at
different traffic scenarios using Hamiltonian analysis. In this paper, we
investigate the properties of the unconstrained problem and provide conditions
under which different combination of the state and control constraints become
active. We present a condition-based computational framework that improves on
the standard iterative solution procedure of the constrained Hamiltonian
analysis. Finally, we derive a closed-form analytical solution of the
constrained optimal control problem and validate the proposed framework using
numerical simulation. The solution can be derived without any recursive steps,
and thus it is appropriate for real-time implementation on-board the CAVs.
