论文标题
基于凸优化的节能火车控制模型的精确性
On the Exactness of an Energy-efficient Train Control model based on Convex Optimization
论文作者
论文摘要
在本文中，我们证明了基于凸优化的节能列车控制（EETC）模型的精确性证明。精确性证明表明，凸优化模型将与进行凸松弛的初始模型共享相同的优化结果。我们首先展示了如何进行初始非凸模模型的放松，并提供分析以表明弛豫是凸的约束，而放松模型是凸模型。随后，我们证明了放松的凸模型将始终在初始相等性约束上实现其最佳解决方案，并且通过凸优化实现的最佳解决方案将与初始非convex模型获得的最佳解决方案相同。基于具有陡峭梯度的典型城市铁路系统进行了数值验证。该论文的结果将灯光放在凸的进一步应用上优化对节能的火车控制以及与低碳运输系统的操作和控制有关的相关区域。
In this paper, we demonstrate the exactness proof for the energy-efficient train control (EETC) model based on convex optimization. The proof of exactness shows that the convex optimization model will share the same optimization results with the initial model on which the convex relaxations are conducted. We first show how the relaxation on the initial non-convex model is conducted and provide analysis to show that the relaxations are convex constraints and the relaxed model is thus a convex model. Subsequently, we prove that the relaxed convex model will always achieve its optimal solution on the initial equality constraints and the optimal solution achieved by convex optimization will be the same as the one obtained by the initial non-convex model and the relaxations applied are exact. A numerical verification has been conducted based on a typical urban rail system with a steep gradient. The results of this paper shed lights on further applications of convex optimization on energy-efficient train control and relevant areas related to operation and control of low-carbon transportation systems.
