Receding Horizon Control of Perturbed Railway Network Operation

Abstract

Railway networks, such as the one in the Netherlands, form an important means of transportation, both for passengers, as well as for transporting goods. Train services carrying passengers often run according to a predefined schedule or timetable. When those train services are delayed, for example due to accidents or malfunctioning rolling stock, the affected train may not be able to run according to schedule any longer. When the railway network is dense and hosts different kinds of services, such as local and intercity services, this initial delay is easily passed on to other train services in the network, due to different stopping patterns and drive speeds. Human dispatchers, possibly aided by computer systems, make temporary modifications to the way the network is used by the trains running in the region of the disturbance. However, due to the high complexity and the limited time, these decisions may be optimal for only the designated area of the dispatcher, but far from optimal from a network perspective. Therefore, a railway network operator could have a major benefit from a system able to compute globally optimal decisions in the case of disturbances. This thesis is written as part of the development of such a system. Specifically, this project aims at applying Model Predictive Control (MPC) to railway networks. In MPC, a model of the system is used to predict the future behaviour of the system within a prediction horizon. The principle of receding horizon control is employed to compute an optimal future input sequence, such that a certain cost is minimized. This cost is the total delay in the network within the prediction horizon. The inputs of the controlled system are associated to the order of a train pair on a track. Train orders can be swapped at stations and junctions. As there are many of those points present in the network, swapping orders offers the most possibilities and is effective in a wide range of delay scenarios. Therefore, in this thesis only order swaps are considered. The system is modelled within a max-plus algebraic framework, which allows for a structured representation and systematic approach, where the latter is especially useful for future endeavours to exploit max-plus system theory, such that for example model reduction can be applied to the generally very large railway models. The algorithm presented in this thesis forms the basis for an MPC algorithm for railway networks. The development of a tailor made receding horizon control algorithm for railway networks, has not been carried out before. First an extension of the existing maxplus linear model is presented, such that a model which is uncertain in the parameters is obtained. This model already contains controllable train orders. The problem of finding the optimal order swaps, such that the total delay in the network is minimal, can be written as a Mixed Integer Linear Programming problem. Several test cases were derived to highlight the various aspects of the receding horizon control algorithm, such as how it copes with different parameter estimations at various points in time. Through the use of a time-based control horizon, a significant reduction in computation time was achieved an provides a very good method to overcome the computational complexity encountered during optimal control of railway networks. Although the prediction horizon is defined in the discrete event domain, the algorithm is easily modified to also contain a time-based prediction horizon, allowing for more freedom in tuning of the prediction horizon and thus also computation times.