Optimal energy-efficient control of high speed train with speed limit constraints

This paper deals with the optimal energy-efficient control strategy of high speed train by means of the maximum principle with the speed limit constraints. Considering the variation and jump regulations of the co-state variable in two cases (with speed limit and without considering the speed limit), two types of transition diagrams are given respectively. According to the transition diagram, the types of transitions with touching the speed limit are classified into four base cases and other transitions are derived or combined from these four base cases. On this basis, the relationship between optimal operation and flat-out operation is discussed. Optimal operation with speed limit is close to the flat-out operation along with the decreasing of the operation time.