Optimization Techniques Applied to Railway Systems

The problem that we study in this Master thesis is the energy minimization of railway systems, where the objective is to find the optimal speed profiles that minimize the consumption of a given journey. We first develop a model that takes into account all the constraints that the problem presents unlike in existing works. Given the difficulty of the problem an analytical solution is beyond our scope so we propose two different numerical methods to tackle the optimal control problem. These methods do not require parameter tuning, which makes them suitable for implementation in real systems. Optimal control techniques play a significant role in many different areas, such as chemistry, aerospace industry, and biomedicine. Many engineering problems concerning energy consumption can be solved by applying these methods. It gives interesting information about the theoretical properties of the problem in hand and it also provides tools to obtain solutions that are applicable to the industry. The main contribution of the thesis are (i) develop a new model that captures closely the dynamics of the train (ii) for an arbitrary starting point we approximate the infinite dimensional control problem with a finite dimensional optimization, which can be efficiently solved numerically (iii) we then model the problem using Dynamic Programming (DP) based approach, (iv) implemented the algorithms in a train simulator developed by INGETEAM. The DP approach allows to solve the optimization problem for all possible initial starting points at once. This is a more computationally expensive problem that could be solved offline and which would allow the driver to react fast to any new circumstance in the course of the trip. The simulator shows that for a typical trip in a major city in Europe the energy reduction with respect to the currently implemented speed profile could be up to % 24.