In this paper, we provide a decentralized theoretical framework for coordination of connected and automated vehicles (CAVs) at different traffic scenarios. The framework includes: (1) an upper-level optimization that yields for each CAV its optimal time trajectory and lane to pass through a given traffic scenario while alleviating congestion; and (2) a low-level optimization that yields for each CAV its optimal control input (acceleration/deceleration). We provide a complete, analytical solution of the low-level optimization problem that includes the rear-end, speed-dependent safety constraint. Furthermore, we provide a problem formulation for the upper-level optimization in which there is no duality gap. The latter implies that the optimal time trajectory for each CAV does not activate any of the state, control, and safety constraints of the low-level optimization, thus allowing for online implementation. Finally, we present a geometric duality framework with hyperplanes to derive the condition under which the optimal solution of the upper-level optimization always exists. We validate the effectiveness of the proposed theoretical framework through simulation.

在本文中，我们提供了一种分散的理论框架，用于在不同交通场景下协调互联和自动驾驶汽车（CAV）。该框架包括：（1）上层优化，可为每个CAV提供通过给定交通场景的最佳时间轨迹和车道，同时缓解拥堵；（2）低级优化，它为每个CAV产生其最佳控制输入（加速/减速）。我们为低级优化问题提供了完整的分析解决方案，其中包括后端，速度相关的安全约束。此外，我们为不存在对偶间隙的上层优化提供了问题表述。后者暗示每个CAV的最佳时间轨迹不会激活任何状态，控制，和低级优化的安全性约束，从而允许在线实施。最后，我们提出了一个具有超平面的几何对偶框架，以得出始终存在上层优化的最优解的条件。我们通过仿真验证了所提出的理论框架的有效性。