A max-algebra solution to the supervisory control problem for real-time discrete event systems

  • Darren D. Cofer
  • Vijay K. Garg
The Max-Plus Algebraic Approach
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 199)


For timed systems the supervisory control problem is to impose delays on controllable events to modify system behavior to meet some specified performance goal. Using the tools of max-algebra it is possible to compute the uncontrolled behavior of a timed event graph, define a specification for some new desired behavior, and determine whether the specification can be realized by any supervisor given the set of controllable events. When the desired behavior cannot be realized (i.e, it is uncontrollable), a minimally restrictive behavior which meets the original specification always exists. All of these concepts have direct analogy in the control of untimed automata.


Controllable Event Acceptable Behavior Firing Sequence Acceptable Region Time Event Graph 
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Copyright information

© Springer-Verlag London Limited 1994

Authors and Affiliations

  • Darren D. Cofer
    • 1
  • Vijay K. Garg
    • 1
  1. 1.Department of Electrical and Computer EngineeringUniversity of TexasAustinUSA

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