  We address the problem of optimally controlling connected and automated
vehicles (CAVs) crossing an urban intersection without any explicit traffic
signaling, so as to minimize energy consumption subject to a throughput
maximization requirement. We show that the solution of the throughput
maximization problem depends only on the hard safety constraints imposed on
CAVs and its structure enables a decentralized optimal control problem
formulation for energy minimization. We present a complete analytical solution
of these decentralized problems and derive conditions under which feasible
solutions satisfying all safety constraints always exist. The effectiveness of
the proposed solution is illustrated through simulation which shows substantial
dual benefits of the proposed decentralized framework by allowing CAVs to
conserve momentum and fuel while also improving travel time.
