# Optimal and model predictive control of railway systems

Project members: | dr.ir. T.J.J. van den Boom (Ton), prof.dr.ir. B. De Schutter (Bart) |
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Keywords: | Model predictive control, Transportation and infrastructure |

In this project we extend the model predictive control framework (MPC), which is a very popular controller design method in the process industry, to railway systems. Usually MPC uses linear (or nonlinear) discrete-time models. However, railway networks and subway networks cannot adequately be described by such models.

First, we have introduced a modeling framework for railway systems with both hard and soft connection constraints. A typical example of a hard connection constraint in a railway context is when a train should give a guaranteed connection to another train. However, in some cases (e.g., if there are delays) we could allow a train to depart although not all trains to which it should give connections according to the schedule have arrived at the station: if some of these trains have a too large delay, then it is sometimes better -- from a global performance viewpoint -- to let the train depart anyway in order to prevent an accumulation of delays in the network. Of course, missed connections lead to a penalty due to dissatisfied passengers or due to compensations that have to be paid. Synchronization constraints that may be broken (but at a cost) are called soft connection constraints. We also consider an extra degree of freedom for the control to recover from delays by letting trains run faster than their nominal speed if necessary. Of course, this control action will also lead to extra costs (due to increased energy consumption or faster wear of the material).

Next, we have extended the MPC framework to railway systems while still retaining the attractive features of conventional MPC. The main aim of the control is to obtain optimal transfer coordination and/or to recover from delays in an optimal way by breaking connections and/or letting some trains run faster than usual (both at a cost). In general the MPC control design problem for railway systems leads to a nonlinear non-convex optimization problem. We have shown that the optimal MPC strategy can be computed using extended linear complementarity problems or integer programming algorithms.

Other examples of systems with both hard and soft synchronization constraints for which this approach can be used are subway networks and logistic operations.