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.

联网和自动驾驶汽车 (CAV) 为提高能源效率、交通流量和安全性提供了最有趣的机会。在早期的工作中，我们使用哈密顿量解决了 CAV 在不同交通场景下的约束最优协调问题分析。在本文中，我们研究了无约束问题的性质，并提供了状态和控制约束的不同组合变得活跃的条件。我们提出了一个基于条件的计算框架，它改进了约束哈密顿分析的标准迭代求解程序。最后，我们推导出约束最优控制问题的封闭形式解析解，并使用数值模拟验证所提出的框架。该解决方案无需任何递归步骤即可推导出来，因此适合在 CAV 上实时实施。