Computational approach for optimal train control based on minimum controller duration

In this paper, we introduce a computational approach for solving optimal driving strategies for trains in which the controllers action are confined to select from discrete modes. Since the controllers operate in succession, in order to avoid the undesirable Zeno phenomenon, we assume that the only one controller can be selected at a time and each active controller duration requires a minimum non-negligible amount time which lead to this problem can not be solved using conventional optimization techniques. To overcome this difficulty, by performing a time-scaling transformation approach and introducing a new binary relaxation, we convert the optimal train control problem into an equivalent optimization problem only with continuous decision variables. We then use a coercive smoothed penalty-based approach to construct a sequence of bound constrained optimization problem, then a novel gradient-based stochastic search method is applying to decrease the computation cost of problem. Numerical examples show that our algorithm is efficient in finding global optimal solution.