  In this paper, we establish a decentralized optimal control framework for
connected and automated vehicles (CAVs) crossing multiple adjacent, multi-lane
signal-free intersections to minimize energy consumption and improve traffic
throughput. Our framework consists of two layers of planning. In the
upper-level planning, each CAV computes its optimal arrival time at each
intersection recursively along with the optimal lane to improve the traffic
throughput. In the low-level planning, we formulate an energy-optimal control
problem with interior-point constraints, the solution of which yields the
optimal control input (acceleration/deceleration) of each CAV to cross the
intersections at the time specified by the upper-level planning. Moreover, we
extend the results of the proposed bi-level framework to include a bounded
steady-state error in tracking the optimal position of the CAVs. Finally, we
demonstrate the effectiveness of the proposed framework through simulation for
symmetric and asymmetric intersections and comparison with traditional
signalized intersections.
