Computation of controllable and coobservable sublanguages in decentralized supervisory control via communication



In decentralized supervisory control, several local supervisors cooperate to accomplish a common goal (specification). Controllability and coobservability are the key conditions to achieve a specification in the controlled system. We construct a controllable and coobservable sublanguage of the specification by using additional communications between supervisors. Namely, we extend observable events of local supervisors via communication and apply a fully decentralized computation of local supervisors. Coobservability is then guaranteed by construction. Sufficient conditions to achieve the centralized optimal solution are discussed. Our approach can be used for both prefix-closed and non-prefix-closed specifications.


Discrete-event systems Decentralized supervisory control Coobservability Separability Communication 


  1. Barrett G, Lafortune S (2000) Decentralized supervisory control with communicating controllers. IEEE Trans Autom Control 45(9):1620–1638MathSciNetCrossRefMATHGoogle Scholar
  2. Brandt RD, Garg V, Kumar R, Lin F, Marcus SI, Wonham WM (1990) Formulas for calculating supremal controllable and normal sublanguages. Syst Control Lett 15(2):111–117MathSciNetCrossRefMATHGoogle Scholar
  3. Bravo H, Da Cunha A, Pena P, Malik R, Cury J (2012) Generalised verification of the observer property in discrete event systems. In: WODES, Mexico, pp 337–342Google Scholar
  4. Cai K, Zhang R, Wonham WM (2015) Relative observability of discrete-event systems and its supremal sublanguages. IEEE Trans Autom Control 60(3):659–670MathSciNetCrossRefGoogle Scholar
  5. Cassandras C, Lafortune S (2008) Introduction to discrete event systems, 2nd edn, SpringerGoogle Scholar
  6. Chakib H, Khoumsi A (2011) Multi-decision supervisory control: parallel decentralized architectures cooperating for controlling discrete event systems. IEEE Trans Autom Control 56(11):2608–2622MathSciNetCrossRefGoogle Scholar
  7. Fa J, Yang X, Zheng Y (1993) Formulas for a class of controllable and observable sublanguages larger than the supremal controllable and normal sublanguage. Syst Control Lett 20(1):11–18MathSciNetCrossRefMATHGoogle Scholar
  8. Feng L (2007) Computationally efficient supervisor design for discrete-event systems. Ph.D. thesis, University of Toronto, OntarioGoogle Scholar
  9. Feng L, Wonham W (2010) On the computation of natural observers in discrete-event systems. Discrete Event Dynamic Systems 20(1):63–102MathSciNetCrossRefMATHGoogle Scholar
  10. Jiang S, Kumar R (2000) Decentralized control of discrete event systems with specializations to local control and concurrent systems. IEEE Trans Syst Man Cybern B Cybern 30(5):653–660CrossRefGoogle Scholar
  11. Jiang S, Kumar R, Garcia HE (2003) Optimal sensor selection for discrete-event systems with partial observation. IEEE Trans Autom Control 48(3):369–381MathSciNetCrossRefGoogle Scholar
  12. Komenda J, Marchand H, Pinchinat S (2006) A constructive and modular approach to decentralized supervisory control problems. IFAC Proceedings Volumes 39 (17):111–116. 3rd IFAC Workshop on Discrete-Event System DesignCrossRefGoogle Scholar
  13. Komenda J, Masopust T (2013) A bridge between decentralized and coordination control. In: Allerton conference on communication, control, and computing, pp 966–972Google Scholar
  14. Komenda J, Masopust T, van Schuppen J (2011) Synthesis of controllable and normal sublanguages for discrete-event systems using a coordinator. Syst Control Lett 60(7):492–502Google Scholar
  15. Komenda J, Masopust T, van Schuppen J (2012) On conditional decomposability. Syst Control Lett 61(12):1260–1268Google Scholar
  16. Komenda J, Masopust T, van Schuppen J (2012) Supervisory control synthesis of discrete-event systems using a coordination scheme. Automatica 48(2):247–254Google Scholar
  17. Komenda J, Masopust T, van Schuppen J (2015) Coordination control of discrete-event systems revisited. Discrete Event Dyn Syst 25(1–2):65–94Google Scholar
  18. Komenda J, Masopust T, van Schuppen J (2015) Relative observability in coordination control. In: IEEE international conference on automation science and engineering (CASE), pp 75–80Google Scholar
  19. Komenda J, van Schuppen JH (2005) Modular antipermissive control of discrete-event systems. IFAC World Congress 38(1):97–102Google Scholar
  20. Komenda J, van Schuppen JH (2008) Modular control of discrete-event systems with coalgebra. IEEE Trans Autom Control 53(2):447–460Google Scholar
  21. Kozák P, Wonham WM (1995) Fully decentralized solutions of supervisory control problems. IEEE Trans Autom Control 40(12):2094–2097MathSciNetCrossRefMATHGoogle Scholar
  22. Kozen D (1977) Lower bounds for natural proof systems. In: FOCS, pp 254–266Google Scholar
  23. Kumar R, Garg VK (1995) Optimal supervisory control of discrete event dynamical systems. SIAM J Control Optim 33(2):419–439MathSciNetCrossRefMATHGoogle Scholar
  24. Kumar R, Takai S (2007) Inference-based ambiguity management in decentralized decision-making: decentralized control of discrete event systems. IEEE Trans Autom Control 52(10):1783–1794MathSciNetCrossRefGoogle Scholar
  25. Lafortune S, Chen E (1990) The infimal closed controllable superlanguage and its application in supervisory control. IEEE Trans Autom Control 35(4):398–405MathSciNetCrossRefMATHGoogle Scholar
  26. Lee SH, Wong K (2002) Structural decentralized control of concurrent discrete-event systems. Eur J Control 8(5):477–491CrossRefMATHGoogle Scholar
  27. Lin L, Stefanescu A, Su R, Wang W, Shehabinia A (2014) Towards decentralized synthesis: Decomposable sublanguage and joint observability problems. In: American control conference, pp 2047–2052Google Scholar
  28. Malik R (2016) Programming a fast explicit conflict checker. In: WODES, pp 438–443Google Scholar
  29. Pena P, Cury J, Lafortune S (2009) Verification of nonconflict of supervisors using abstractions. IEEE Trans Autom Control 54(12):2803–2815MathSciNetCrossRefGoogle Scholar
  30. Pena P, Cury J, Malik R, Lafortune S (2010) Efficient computation of observer projections using OP-verifiers. In: WODES, pp 416–421Google Scholar
  31. Ramadge P, Wonham W (1987) Supervisory control of a class of discrete event processes. SIAM J Control Optim 25(1):206–230MathSciNetCrossRefMATHGoogle Scholar
  32. Ricker S, Rudie K (2000) Know means no: incorporating knowledge into discrete-event control systems. IEEE Trans Autom Control 45(9):1656–1668MathSciNetCrossRefMATHGoogle Scholar
  33. Ricker SL, Rudie K (2007) Knowledge is a terrible thing to waste: using inference in discrete-event control problems. IEEE Trans Autom Control 52(3):428–441MathSciNetCrossRefGoogle Scholar
  34. Rohloff K, Khuller S, Kortsarz G (2006) Approximating the minimal sensor selection for supervisory control. Discrete Event Dynamic Systems 16(1):143–170MathSciNetCrossRefMATHGoogle Scholar
  35. Rohloff K, Lafortune S (2005) PSPACE-completeness of modular supervisory control problems. Discrete Event Dynamic Systems 15:145–167MathSciNetCrossRefMATHGoogle Scholar
  36. Rohloff K, Yoo T, Lafortune S (2003) Deciding co-observability is PSPACE-complete. IEEE Trans Autom Control 48(11):1995–1999MathSciNetCrossRefGoogle Scholar
  37. Rudie K, Lafortune S, Lin F (2003) Minimal communication in a distributed discrete-event system. IEEE Trans Autom Control 48(6):957–975MathSciNetCrossRefGoogle Scholar
  38. Rudie K, Wonham W (1992) Think globally, act locally: decentralized supervisory control. IEEE Trans Autom Control 37(11):1692–1708MathSciNetCrossRefMATHGoogle Scholar
  39. Rudie K, Wonham WM (1990) The infimal prefix-closed and observable superlanguage of given language. Syst Control Lett 15(5):361–371MathSciNetCrossRefMATHGoogle Scholar
  40. Rudie K, Wonham WM (1990) Supervisory control of communicating processes. In: Protocol specification, testing and verification X, pp 243–257Google Scholar
  41. Schmidt K, Breindl C (2008) On maximal permissiveness of hierarchical and modular supervisory control approaches for discrete event systems. In: WODES, pp 462–467Google Scholar
  42. Schmidt K, Breindl C (2011) Maximally permissive hierarchical control of decentralized discrete event systems. IEEE Trans Autom Control 56(4):723–737MathSciNetCrossRefGoogle Scholar
  43. Takai S (1998) On the language generated under fully decentralized supervision. IEEE Trans Autom Control 43(9):1253–1256MathSciNetCrossRefMATHGoogle Scholar
  44. Takai S, Kumar R (2008) Synthesis of inference-based decentralized control for discrete event systems. IEEE Trans Autom Control 53(2):522–534MathSciNetCrossRefGoogle Scholar
  45. Takai S, Ushio T (2003) Effective computation of an L m(G)-closed, controllable, and observable sublanguage arising in supervisory control. Syst Control Lett 49(3):191–200CrossRefMATHGoogle Scholar
  46. Thistle J (2005) Undecidability in decentralized supervision. Syst Control Lett 54(5):503–509MathSciNetCrossRefMATHGoogle Scholar
  47. Tripakis S (2004) Undecidable problems of decentralized observation and control on regular languages. Inf Process Lett 90(1):21–28MathSciNetCrossRefMATHGoogle Scholar
  48. Wang W, Girard AR, Lafortune S, Lin F (2011) On codiagnosability and coobservability with dynamic observations. IEEE Trans Autom Control 56(7):1551–1566MathSciNetCrossRefGoogle Scholar
  49. Wang W, Lafortune S, Lin F (2008) Optimal sensor activation in controlled discrete event systems. In: Conference on decision and control, pp 877–882. IEEEGoogle Scholar
  50. Willner Y, Heymann M (1991) Supervisory control of concurrent discrete-event systems. Int J Control 54(5):1143–1169MathSciNetCrossRefMATHGoogle Scholar
  51. Wong K (1998) On the complexity of projections of discrete-event systems. In: WODES, pp 201–206Google Scholar
  52. Wonham W (2012) Supervisory control of discrete-event systems. University of Toronto,
  53. Yin X, Lafortune S (2016) Synthesis of maximally permissive supervisors for partially-observed discrete-event systems. IEEE Trans Autom Control 61(5):1239–1254MathSciNetCrossRefGoogle Scholar
  54. Yoo T, Lafortune S (2002) A general architecture for decentralized supervisory control of discrete-event systems. Discrete Event Dynamic Systems 12(3):335–377MathSciNetCrossRefMATHGoogle Scholar
  55. Yoo T, Lafortune S (2004) Decentralized supervisory control with conditional decisions: supervisor existence. IEEE Trans Autom Control 49(11):1886–1904MathSciNetCrossRefGoogle Scholar
  56. Zhong H, Wonham WM (1990) On the consistency of hierarchical supervision in discrete-event systems. IEEE Trans Autom Control 35(10):1125–1134MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute of MathematicsCzech Academy of SciencesBrnoCzech Republic
  2. 2.Institute of Theoretical Computer Science and Center of Advancing Electronics Dresden (cfaed)DresdenGermany

Personalised recommendations