Reference:
T.J.J. van den Boom,
B. Kersbergen, and
B. De Schutter,
"Structured modeling, analysis, and control of complex railway
operations," Proceedings of the 51st IEEE Conference on Decision
and Control, Maui, Hawaii, pp. 7366-7371, Dec. 2012.
Abstract:
In this paper we discuss the rescheduling of trains on a large-scale
railway network in the case of perturbations using a max-plus-linear
system description. We study the structure of the system matrices and
derive how this structure can be manipulated by the control variables.
In addition, we show that this leads to a system matrix that is affine
in the control variables and the timing parameters. We also consider
additional constraints for scheduling trains on multiple tracks and
constraints for joining and splitting trains.