Timed Petri Nets in Hybrid Systems: Stability and SupervisoryControl

  • Authors:
  • Xenofon D. Koutsoukos;Kevin X. He;Michael D. Lemmon;Panos J. Antsaklis

  • Affiliations:
  • Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556/ xkoutsou@maddog.ee.nd.edu;Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556/ xhe@maddog.ee.nd.edu;Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556/ lemmon@maddog.ee.nd.edu;Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN 46556/ antsakli@maddog.ee.nd.edu

  • Venue:
  • Discrete Event Dynamic Systems
  • Year:
  • 1998

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Abstract

In this paper, timed Petri nets are used to model andcontrol hybrid systems. Petri nets are used instead of finiteautomata primarily because of the advantages they offer in dealingwith concurrency and complexity issues. A brief overview of existingresults on hybrid systems that are based on Petri nets is firstpresented. A class of timed Petri nets named programmable timedPetri nets (PTPN) is then used to model hybrid systems. Usingthe PTPN, the stability and supervisory control of hybrid systemsare addressed and efficient algorithms are introduced. In particular,we present sufficient conditions for the uniform ultimate boundnessof hybrid systems composed of multiple linear time invariantplants which are switched between using a logical rule describedby a Petri net. This paper also examines the supervisory controlof a hybrid system in which the continuous state is transferedto a region of the state space in a way that respects safetyspecifications on the plant‘s discrete and continuous dynamics.