A Coalgebraic Approach to Supervisory Control of Partially Observed Mealy Automata

  • Jun Kohjina
  • Toshimitsu Ushio
  • Yoshiki Kinoshita
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6859)


Supervisory control is a logical control method of discrete event systems introduced by Ramadge and Wonham. We propose a novel coalgebraic formulation of a supervisory control problem and design a controller called supervisor satisfying a given specification under partial observations. In this paper, plants, specifications, and supervisors are modeled by Mealy automata, automata, and Moore automata, respectively. We define a composition of a supervisor and a plant coinductively, which is called a supervisory composition, to represent a behavior of the controlled plant. We formulate a supervisory control problem using the supervisory composition. We define two relations: a partial bisimulation relation and a modified normal relation. We show that these relations are related to the controllability/observability and the modified normality which are the key notions in the supervisory control theory.


discrete event systems supervisory control coalgebra 


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  1. 1.
    Cassandras, C., Lafortune, S.: Introduction to Discrete Event Systems. Springer, Heidelberg (2008)zbMATHCrossRefGoogle Scholar
  2. 2.
    Cieslak, R., Desclaux, C., Fawaz, A., Varaiya, P.: Supervisory control of discrete-event processes with partial observations. IEEE Transactions on Automatic Control 33(3), 249–260 (1988)zbMATHCrossRefGoogle Scholar
  3. 3.
    Hansen, H.: Coalgebraic Modelling: Applications in Automata theory and Modal logic. Ph.D. thesis (2009)Google Scholar
  4. 4.
    Komenda, J., van Schuppen, J.: Control of discrete-event systems with partial observations using coalgebra and coinduction. Discrete Event Dynamic Systems 15(3), 257–315 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Komenda, J., van Schuppen, J.: Modular control of discrete-event systems with coalgebra. IEEE Transactions on Automatic Control 53(2), 447–460 (2008)CrossRefGoogle Scholar
  6. 6.
    Lin, F., Wonham, W.: On observability of discrete-event systems. Information Sciences 44(3), 173–198 (1988)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Ramadge, P., Wonham, W.: Supervisory control of a class of discrete event processes. SIAM J. Control & Optimiz. 25(1), 206–230 (1987)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Rutten, J.: Coalgebra, concurrency and control. CWI. Software Engineering (SEN) (R 9921), 1–31 (1999)Google Scholar
  9. 9.
    Rutten, J.J.: Universal coalgebra: a theory of systems. Theoretical Computer Science 249(1), 3–80 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Ushio, T., Takai, S.: Supervisory control of discrete event systems modeled by Mealy automata with nondeterministic output functions. In: American Control Conference, pp. 4260–4265 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jun Kohjina
    • 1
  • Toshimitsu Ushio
    • 1
  • Yoshiki Kinoshita
    • 2
  1. 1.Graduate School of Engineering ScienceOsaka UniversityJapan
  2. 2.National Institute of Advanced Industrial Science and TechnologyJapan

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