This research investigates the optimal control problem of heavy haul train for the minimization of longitudinal forces. As the heavy haul train is much heavier and longer than ordinary train, the in-train forces should be carefully manipulated to reduce the train’s maintenance cost and, most importantly, to ensure operation safety. Specifically, the limitations of pneumatically controlled braking system increase the need for the optimal control strategy to accounting for future grades, speed restrictions and uncertain disturbances. In this article, the stochastic dynamic programming model is adopt to set up a rigorous mathematical formulation for heavy haul train control, and approximate dynamic programming algorithm with lookup table representation is introduced to find the optimal solution of the considered problem. By handling the existed uncertainties in a mathematical way, the post-decision state variable is utilized to represent the state of the heavy haul train after we have made a control decision...
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