Literature

One last time in this course we refer to [1], a comprehensive and popular introduction do discrete event systems. A short introduction to the framework (max,+) algebra can be found (under the somewhat less known name “Dioid algebras”) in Chapter 5.4.

But as a recommendable alternative, (any one of) the a series of papers by Bart de Schutter (TU Delft) and his colleagues can be read instead. For example [2] and [3].

For anyone interested in learning yet more, a beautiful (and freely online) book is [4], which we have also mentioned in the context of Petri nets.

Max-plus algebra is relevant outside the domain of discrete-event systems – it is also investigated in optimization for its connection with piecewise linear/affine functions. Note that the community prefers using the name tropical geometry (to emphasise that they view it as a branch of algebraic geometry). A lovely tutorial is [5].

References

[1]

C. G. Cassandras and S. Lafortune, Introduction to Discrete Event Systems, 3rd ed. Cham: Springer, 2021. Available: https://doi.org/10.1007/978-3-030-72274-6

[2]

B. De Schutter, T. van den Boom, J. Xu, and S. S. Farahani, “Analysis and control of max-plus linear discrete-event systems: An introduction,” Discrete Event Dynamic Systems, vol. 30, no. 1, pp. 25–54, Mar. 2020, doi: 10.1007/s10626-019-00294-w.

[3]

B. De Schutter and T. van den Boom, “Model predictive control for max-plus-linear discrete-event systems: Extended report & Addendum,” Delft University of Technology, Delft, The Netherlands, Technical Report bds:99-10a, Nov. 2000. Available: https://pub.deschutter.info/abs/99_10a.html

[4]

F. Baccelli, G. Cohen, G. J. Olsder, and J.-P. Quadrat, Synchronization and linearity: An algebra for discrete event systems, Web edition. Chichester: Wiley, 2001. Available: https://www.rocq.inria.fr/metalau/cohen/documents/BCOQ-book.pdf

[5]

J. Rau, “A First Expedition to Tropical Geometry,” Apr. 2017. Available: https://www.math.uni-tuebingen.de/user/jora/downloads/FirstExpedition.pdf