Analytical Solution To The Minimum Fuel Consumption Optimization Problem With The Existence Of A Traffic Light

Today's driving patterns consume significant amount of useless energy, especially, when the fuel consumptions while braking, idling and re-accelerating at each traffic light are considered for millions of vehicles. This makes a high level management of driving profile crucial. In this paper; an analytical solution to the fuel consumption minimization problem with the existence of a single traffic light is investigated. The analytical solution is important for on-line implementation and sharing the information of the estimated fuel consumption of the road ahead with other vehicles. Pontryagin's minimum principle is used to calculate the optimal velocity profile. Prior to the calculations, it is assumed that we have the knowledge of starting and ending points of the trip, the position and the operation sequence of the traffic light. In order to make the problem solvable, a simplified vehicle model is used. Furthermore, Willans approximation is utilized for fuel consumption calculations with addition of certain amount of idle speed fuel cost. The vehicle is forced to operate between a feasible torque and speed range. The optimization problem is simulated for an SUV vehicle first on a level road, then on a level road with the traffic light and finally on a road with grade. The results have shown that in addition to operating the vehicle close to its optimal point, it is possible to avoid the consumption of useless fuel due to the braking, idling and re-acceleration phases of a traffic light.