  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.
