Discrete Event Dynamic Systems

, Volume 19, Issue 1, pp 1–30

Closed-loop Live Marked Graphs under Generalized Mutual Exclusion Constraint Enforcement

  • Francesco Basile
  • Laura Recalde
  • Pasquale Chiacchio
  • Manuel Silva


Enforcing a supervisory control policy to avoid forbidden states on a discrete event system modeled by a Petri net may result in a non live system. This may happen even if the admissible states are specified by Generalized Mutual Exclusion Constraints (GMECs). This leads to the problem of synthesizing a maximally permissive control policy preserving liveness of the system under a GMEC. This problem is very interesting in practice, but difficult even for a restricted class of systems. In this paper, we focus on systems which can be modeled as live and safe Marked Graphs (MGs). On such systems, when some of the transitions are uncontrollable, a GMEC can be forced by a monitor place if a not maximally permissive policy is accepted, otherwise a more complex control has to be adopted. Anyway, liveness of the closed-loop system (plant plus control) is not guaranteed. Two sufficient conditions to verify the closed-loop liveness of a live and safe MG plant controlled by a monitor are derived. A sufficient condition for closed loop liveness of MGs where a GMEC has been enforced on is derived. In addition, a set of predicates is provided that enforces, in a maximally permissive way, a GMEC while preserving closed-loop liveness on live and safe MG systems under some restrictions.


Supervisory control Closed-loop liveness Generalized mutual exclusion constraint Monitor places Marked graphs 


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Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Francesco Basile
    • 1
  • Laura Recalde
    • 2
  • Pasquale Chiacchio
    • 1
  • Manuel Silva
    • 2
  1. 1.Dipartimento di Ingegneria dell’Informazione e Ingegneria ElettricaUniversità degli Studi di SalernoFisciano (SA)Italy
  2. 2.Dep. de Informática e Ingeniería de SistemasZaragozaSpain

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