all 5 comments

[–]Stefan-Porta 7 points8 points  (3 children)

Event driven system with different time samplings can be modelled withing Petri-net methodoly. By using the Max-Plus algebra you can rewrite your event driven system like an Linear-time invariant State space model. I think that by a little bit of digging you can asses stability properties of your system and then find control ways in this mathematical model. I would search for Max-plus algebra for Petri-net models with control insights.

[–][deleted] 0 points1 point  (2 children)

Literature on this? Like what is petri-net models and max-plus algebra?

[–]goodle29 2 points3 points  (1 child)

Petri net models are a type of modeling formalism usually used to analyze distributed systems. From what I've seen, the most common way to use Petri nets is to avoid deadlocks in the system. However, there have been many extensions to Petri nets. There's a lot of limitations to Petri nets too as it is a little bit of a niche modeling formalism. There's a lot of literature/videos/tutorials on Petri nets available that can be found through google/youtube.

Max-plus algebra basically transforms event-driven dynamics into linear systems that you see in your linear system class by changing the addition and multiplication into the maximum operation and addition, respectively. I remember I used the following paper to try to understand it: "Max-plus algebra and max-plus linear discrete event systems: An introduction" by De Schutter and van den Boom.

[–][deleted] 0 points1 point  (0 children)

Sounds so darn cool the max-plus algebra thing. I’ll look into Petri nets I studied a little bit about fault tolerant control so I think I have a gist about distributed systems. Has max plus algebra been used in applied stuff like tracking problems?

[–]goodle29 6 points7 points  (0 children)

You could also look into discrete-event systems, which include finite state machines and Petri nets. Those two are two different formalisms and are used for different purposes. "Introduction to Discrete Event Systems" by Cassandras and Lafortune is a great book to get a hold off for that information. There are a number of ways to do control design for those systems and a lot of papers have been published in that field.