The optimal solution to the energy-efficient train control in a multi-trains system-part 1: the algorithm design

AbstractWhen a train travels in a multi-trains system, the power flow of other trains and the track grades make up the spatial–temporal area (STA) for the train. Finding the optimal solution for the energy-efficient train control problem in STA can help reduce the net energy consumption. This paper studies the analytic method to obtain the optimal solution. In Part 1, we propose an algorithm specifically designed for this problem. The underlying structure of the algorithm is the connection between three optimal states through the optimal feasible strategy. We propose an algebraic method to calculate the optimal feasible strategy and discuss how it intersects with the speed limit. In Part 2, we will discuss the optimality and uniqueness of the optimal feasible strategy. Case studies using data from a real freight railway line are given to demonstrate the effectiveness of the proposed algorithm.KEYWORDS: Optimal train controlenergy savingPontryagin’s maximum principlenet energy consumption Disclosure statementNo potential conflict of interest was reported by the author(s).CRediT authorship contribution statementYu Rao: Conceptualisation, Methodology, Software, Writing-original draft. Xiaoyun Feng: Methodology, Validation. Qingyuan Wang: Supervision, Visualisation. Pengfei Sun: Conceptualisation, Writing-review & editing.Data availability statementThe data that support the findings of this study are available from the corresponding author upon reasonable request.Additional informationFundingThis work was supported by the National Natural Science Foundation of China under grant 62003283 and the National Key Research and Development Program of China under grant 2021YFB2601500.