Optimal driving for vehicle fuel economy under traffic speed uncertainty

Minimizing the amount of fuel consumed by a moving vehicle can be formulated as an optimal control problem that determines the speed profile that the vehicle should follow. The fuel consumption is generally a function of speed and acceleration, and is optimized under external parameters (e.g., road grade or surrounding traffic conditions) known to affect fuel economy. Uncertainty in the traffic conditions, and in particular traffic speed, has seldom been investigated in this context, which may prevent the vehicle from following the optimal speed profile and consequently affect the fuel economy and the journey time. This paper describes two stochastic optimal speed control models for minimizing the fuel consumption of a vehicle traveling over a given stretch of road under a given time limit, where the maximum speed that can be achieved by the vehicle over the journey is assumed to be random and follow a certain probability distribution. The models include chance constraints that either (i) limit the probability that the desired vehicle speed exceeds the traffic speed, or (ii) bound the probability that the journey time limit is violated. The models are then extended into distributionally robust formulations to capture any uncertainties in the probability distribution of the traffic speed. Computational results are presented on the performance of the proposed models and to numerically assess the impact of traffic speed variability and journey duration on the desired speed trajectories: The results affirm that uncertainty in traffic speeds can significantly increase the amount of fuel consumption and the journey time of the speed profiles created by deterministic model. Such increase in journey duration can be mitigated by incorporating the stochasticity at the planning stage using the models described in this paper, and more so with the distributionally robust formulations particularly with higher levels of uncertainty. The solutions themselves generally exhibit low levels of speeds, which ensure the feasibility of the speed profile against any variabilities in the traffic speed.