具有驾驶性能约束的脉冲滑行驾驶：庞特里亚金方法
Pulse-and-Glide Driving with Drivability Constraints: A Pontryagin Approach
摘要：
本文采用庞特里亚金方法分析了不同名义车速下的脉冲滑行行驶。有大量文献支持这样一个事实，即与以恒定速度驾驶相比，脉冲滑行有可能降低油耗，但在各种标称速度下的好处仍然相对未被探索。在文献的基础上，我们制定了一个速度轨迹最优化问题，其中的目标是一个线性标量化的帕累托组合的燃料消耗和平均车速，除了加加速度的二次罚款。通过使用庞特里亚金方法分析这个最优化问题，我们表明：（i）对于每个标称速度，存在对加加速度的临界惩罚，低于该临界惩罚时，最优解是脉冲和滑行，（ii）在没有对加加速度的任何惩罚的情况下，最优脉冲和滑行轨迹无限快地切换，以及（iii）在临界标称速度以上，最优解是稳态速度驾驶而不是脉冲和滑行，不管对混蛋的惩罚如何
英文摘要：
This paper uses Pontryagin methods to analyze pulse-and-glide driving for different nominal vehicle speeds. There is significant literature supporting the fact that pulse-and-glide has the potential to reduce fuel consumption compared to driving at a constant speed, but the benefits at a variety of nominal speeds remain relatively unexplored. Building on the literature, we formulate a speed trajectory optimization problem where the objective is a linearly-scalarized Pareto combination of fuel consumption and average vehicle speed, in addition to a quadratic penalty on jerk. By analyzing this optimization problem using Pontryagin methods, we show that (i) for each nominal speed, there is a critical penalty on jerk below which the optimal solution is pulse-and-glide, (ii) without any penalty on jerk, the optimal pulse-and-glide trajectory switches infinitely fast, and (iii) above a critical nominal velocity, the optimal solution is steady-speed driving rather than pulse-and-glide, regardless of the penalty on jerk.
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