Train energy-efficient operation with stochastic resistance coefficient

Train energy-efficient operation problem applies the optimal control theory to optimize the speed profile between successive stations such that the tracking energy is minimized. Traditional studies show that the optimal speed profile consists of four phases including maximum acceleration, cruising, coasting and maximum braking. Based on the assumption that the resistance coefficients are random variables as the disturbances arising from the weather and locomotive conditions, this paper proposes a stochastic train energy-efficient operation model, and proves that the coasting phase should be replaced by a quasicoasting phase for the optimal speed profile. An efficient iterative algorithm is designed to solve the optimal switching strategy among different phases, and a numerical example is illustrated to show that the stochastic optimization approach can further save energy by 3:68% compared with the traditional studies.