Optimization for train speed trajectory based on Pontryagin's Maximum Principle

Among different energy efficiency improvement technologies for railway transportation, the optimization of speed trajectory is a feasible method with low cost, since there is no need to upgrade the railway infrastructures. This paper proposes a simplified method to find speed trajectory and co-state variables. The method is based on Pontryagin's Maximum Principle (PMP) to minimize tractive energy. Hamiltonian and co-state equation are derived. The design of this paper is based on an ideal model which has no speed limit, gradient, and regenerative braking. Under the necessary condition of PMP, it can obtain acceleration, cruising, coasting, deceleration sections independently using a linear iteration, and then connect them to form full trajectory using the Linking Principle proposed in this paper. The train parameters are determined based on locomotive SS4. The results show that PMP can be applied on optimal train trajectory with minimum energy consumption.