A short introduction to the framework (max,+) algebra can be found (under the somewhat less known name "Dioid algebras") in Chapter 5.4 of the classical (and award-winning) reference

But as a recommendable alternative (any one of) the a series of papers by Bart de Schutter (and his colleagues) can be read instead. For example:

  • De Schutter, Bart, Ton van den Boom, Jia Xu, and Samira S. Farahani. “Analysis and Control of Max-plus Linear Discrete-Event Systems: An Introduction.” Discrete Event Dynamic Systems 30, no. 1 (March 1, 2020): 25–54. https://doi.org/10.1007/s10626-019-00294-w.
  • De Schutter, Bart, and Ton van den Boom. “Model Predictive Control for Max-plus-Linear Discrete-Event Systems: Extended Report & Addendum.” Technical report. Control Systems Engineering. Delft, The Netherlands: Delft University of Technology, November 2000. https://pub.deschutter.info/abs/99_10a.html. (This is an extended version of the equally named journal paper).

For anyone interested in learning yet more, a beautiful (and freely online) book is

In fact, it is the possibility to use MPC for this state-space-like model that makes the whole framework attractive for us, control engineers. Some extensions of this idea are also proposed for hybrid systems.

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. However, that community apparently prefers using the name tropical geometry (to emphasise that they view it as a branch of algebraic geometry). A lovely tutorial is 

Naposledy změněno: středa, 11. října 2023, 10.18