Calculation of the minimum-fuel driving control based on Pontryagin’s maximum principle

•A method to calculate the minimum-fuel driving control of a point-mass vehicle is calculated.•This can take into account distance and time constraints.•Gear shifting, clutch disengagement, and brake control are included with switching conditions.•For a quadratic fuel consumption model, an explicit formula is yielded.

This paper presents a methodology to calculate the minimum-fuel driving control for a point-mass vehicle on a road with constant slope. The main control is the engine torque. Gear shifting, clutch disengagement, and braking are taken into account with a switching condition. The methodology can take into account distance and time constraints. Only longitudinal vehicle dynamics are used in combination with a quasistatic polynomial fuel consumption model. Simulations are given to analyze the optimal driving control and assess the fuel savings for acceleration and deceleration.