Rational semimodules over the max-plus semiring and geometric approach of discrete event systems

Details Rational semimodules over the max-plus semiring and geometric approach of discrete event systems Rational semimodules over the max-plus semiring and geometric approach of discrete event systems

2002-08-02

arxiv.org/abs/math/0208014v2

Kybernetika -- volume 40 (2004), number 2, pages 153--180.

Mathematics

Optimization and Control

24 pages, 9 postscript figures; example in section 4.3 expanded

Scientific paper

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule S^n over a semiring S is rational if it has a generating family that is a rational subset of S^n, S^n being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, rational semimodules are stable under the natural algebraic operations (union, product, direct and inverse image, intersection, projection, etc). We show that the reachable and observable spaces of max-plus linear dynamical systems are rational, and give various examples.

Affiliated with

Also associated with

No associations

Rating

Rational semimodules over the max-plus semiring and geometric approach of discrete event systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Rational semimodules over the max-plus semiring and geometric approach of discrete event systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Rational semimodules over the max-plus semiring and geometric approach of discrete event systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-442044