Keywords: high-speed train dynamics, Bayesian inference, optimization under constraints and uncertainty.

Controlling the energy consumed by our systems has turned to be an important stake in today’s world and especially in the railway domain, since transports constitute one of the largest energy consumers. In the railway sector, the energy consumed by high-speed trains depends on many variables such as the vehicle characteristics, the rolling environment of the train, or its speed profile. To limit the impact of the latter, drivers are asked to follow a target trajectory defined by crossing points along the journey. Nevertheless, we can remark that important differences in energy consumption still exist. The industrial objective of this work is to define a model, able to describe the train dynamics and to propose an optimization method, which aims to minimize the energy consumption under uncertainties. This work is composed of two parts. First of all, two probabilistic models are defined to describe the train longitudinal dynamics (based on a Lagrangian approach) and its energy consumption. This model is fitted using a Bayesian calibration from measurements carried out on commercial trains. Particular attention is paid to the description of the rolling environment of the train and of the vehicle characteristics. Afterwards, the robust optimization of the command under uncertainty is performed using the CMA-ES method to minimize the energy consumed while punctuality, security, and comfort constraints are respected. On the scientific point of view, this work has enabled the development of original methods to introduce non-linear physical and punctuality constraints in a probabilistic framework by means of order relations. The driver's command is chosen as the optimization variable instead of the train speed, as it is often the case in literature. It facilitates the transposition of the developments to real systems. In addition, many energy measurements are used to calibrate and validate the models. The rolling environment and the vehicle characteristics are carefully defined from existing case study. To conclude, algorithms are developed for the robust optimization of the problem including uncertainties on both objective function and constraints.

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