Robust Optimization of Multi-train Energy-efficient and Safe-separation Operation Considering Uncertainty in Train Dynamics

This paper treats the uncertainties in practical train operations as disturbances in train dynamics and proposes a robust optimization method for multi-train operations. First, the indeterministic problem is transformed into a deterministic problem, by linearizing the train dynamics, analyzing the propagation of disturbances, and introducing new state variables. Then, a nonlinear program (NLP) is developed to solve the deterministic problem. The speed profiles of each train are simultaneously optimized to minimize the total traction energy while ensuring safe-separation among adjacent trains. Our results show that operation constraints and absolute safe time headway can always be guaranteed, even in the worst-case scenarios caused by disturbances.