Backward reachability of autonomous max-plus-linear systems

Dieky Adzkiya, Bart De Schutter, Alessandro Abate

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


This work discusses the backward reachability of autonomous Max-Plus-Linear (MPL) systems, a class of continuous-space discrete-event models that are relevant for applications dealing with synchronization and scheduling. Given an MPL system and a continuous set of final states, we characterize and compute its "backward reach tube" and "backward reach sets," namely the set of states that can reach the final set within a given event interval or at a fixed event step, respectively. We show that, in both cases, the computation can be done exactly via manipulations of difference-bound matrices. Furthermore, we illustrate the application of the backward reachability computations over safety and transient analysis of MPL systems.

Original languageEnglish
Title of host publication12th IFAC/IEEE Workshop on Discrete Event Systems, WODES 2104
EditorsJean-Jacques Lesage, Jean-Marc Faure, José E. Ribeiro Cury, Bengt Lennartson
PublisherUnivelt Inc.
Number of pages6
ISBN (Print)9783902823618
Publication statusPublished - 2014
Externally publishedYes
Event12th IFAC/IEEE Workshop on Discrete Event Systems, WODES 2104 - Cachan, France
Duration: 14 May 201416 May 2014

Publication series

NameAdvances in the Astronautical Sciences
ISSN (Print)0065-3438


Conference12th IFAC/IEEE Workshop on Discrete Event Systems, WODES 2104


  • Backward reach tube
  • Backward reachability analysis
  • Difference-bound matrices
  • Max-plus-linear systems
  • Piecewise affine systems
  • Safety and transient analysis


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