Mathematics of Control, Signals and Systems

, Volume 5, Issue 4, pp 365–390 | Cite as

Invertibility of Discrete-Event Dynamic Systems

  • Cüneyt M. Özveren
  • Alan S. Willsky


In this paper we consider a class of Discrete-Event Dynamic Systems (DEDS) modeled as finite-state automata in which only some of the transition events are directly observed. An invertible DEDS is one for which it is possible to reconstruct the entire event string from the observation of the output string. The dynamics of invertibility are somewhat complex, as ambiguities in unobservable events are typically resolved only at discrete intervals and, perhaps, with finite delay. A notion of resiliency or error recovery is developed for invertibility, and polynomial-time tests for invertibility and for resilient invertibility, as well as a procedure for the construction of a resilient inverter, are discussed.

Key words

Automata Invertibility Observability Resiliency Error recovery Discrete-event dynamic systems 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [CDFV]
    R. Cieslak, C. Desclaux, A. Fawaz, and P. Varaiya, Supervisory control of discrete-event processes with partial observations,IEEE Trans. Automat. Control,33 (1988), 249–260.Google Scholar
  2. [LW]
    F. Lin and W. M. Wonham, Decentralized supervisory control of disrete-event systems,Inform. Sci.,44 (1988), 199–224.Google Scholar
  3. [OW1]
    J. S. Ostroff and W. M. Wonham, A temporal logic approach to real time control,Proceedings of the 24th IEEE Conference on Decision and Control, Ft. Lauderdale, FL, 1985, pp. 656–657.Google Scholar
  4. [OW2]
    C. M. Özveren and A. S. Willsky, Observability of discrete event dynamic systems,IEEE Trans. Automat. Control,35 (1990), 797–806.Google Scholar
  5. [OW3]
    C. M. Özveren and A. S. Willsky, Output stabilizability of discrete event dynamic systems,IEEE Trans. Automat. Control,36 (1991), 925–935.Google Scholar
  6. [OWA]
    C. M. Özveren, A. S. Willsky, and P. J. Antsaklis, Stability and stabilizability of discrete-event dynamic systems,J. Assoc. Comput. Mach.,38 (1991), 730–752.Google Scholar
  7. [PW]
    W. W. Peterson and E. J. Weldon, Jr.,Error-Correcting Codes, MIT Press, Cambridge, MA, 1972.Google Scholar
  8. [RW1]
    P. J. Ramadge and W. M. Wonham, Modular feedback logic for discrete-event systems,SIAM J. Control Optim.,25 (1987), 1202–1218.Google Scholar
  9. [RW2]
    P. J. Ramadge and W. M. Wonham, Supervisory control of a class of discrete-event processes,SIAM J. Control Optim.,25 (1987), 206–230.Google Scholar
  10. [VW]
    A. F. Vaz and W. M. Wonham, On supervisor reduction in discrete-event systems,Internat. J. Control,44 (1986), 475–491.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1992

Authors and Affiliations

  • Cüneyt M. Özveren
    • 1
  • Alan S. Willsky
    • 2
  1. 1.Telecommunications and NetworkingDigital Equipment CorporationLittletonUSA
  2. 2.Laboratory for Information and Decision Systems, MITCambridgeUSA

Personalised recommendations