Abstract
Failure diagnosability has been widely studied for discrete event system (DES) models because of modeling simplicity and computational efficiency due to abstraction. In the literature it is often held that for diagnosability, such models can be used not only for systems that fall naturally in the class of DES but also for the ones traditionally treated as continuous variable dynamic systems. A class of algorithms for failure diagnosability of DES models has been successfully developed for systems where fairness is not a part of the model. These algorithms are based on detecting cycles in the normal and the failure model that look identical. However, there exist systems with all transitions fair where the diagnosability condition that hinges upon this feature renders many failures non-diagnosable although they may actually be diagnosable by transitions out of a cycle. Hence, the diagnosability conditions based on cycle detection need to be modified to hold for many real-world systems where all transitions are fair. In this work, however, it is shown by means of an example that a system may have some transitions fair and some unfair. A new failure diagnosability mechanism is proposed for DES models with both fair and unfair transitions. Time complexity for deciding diagnosability of DES models with fair and unfair transitions is analyzed and compared with the time complexities of other DES diagnosability analysis methods reported in the literature.
Similar content being viewed by others
References
Alur R, Henzinger TA, Ho P-H (1996) Automatic symbolic verification of embedded systems. IEEE Trans Softw Eng 22(0000):181–201
Alur R, Courcoubetis C, Henzinger TA, Ho P-H (1993) Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems. In: Hybrid systems, LNCS 736. Springer, New York, pp 209–229
Bavishi S, Chong E (1994) Automated fault diagnosis using a discrete event systems framework. In: IEEE int symp intelligent control, pp 213–218
Biswas S, Karfa C, Kanwar H, Sarkar D, Mukhopadhyay S, Patra A (2006) Fairness of transitions in diagnosability analysis of hybrid systems. In: American control conference-2006, pp 2664–2669
Chutinan A, Krogh B (1999) Verification of polyhedral-invariant hybrid automata using polygonal flow pipe approximations. In: International workshop on hybrid systems: computation and control, pp 76–90
Debouk R (2000) Failure diagnosis of decentralized discrete event systems. Ph.D. dissertation, Elec. Eng. Comp. Sci. Dept., University of Michigan, Ann Arbor
Forstner D, Lunze J (2001) Discrete-event models of quantized systems for diagnosis. Int J Control 74(7):690–700
Frehse G (2005) Phaver: algorithmic verification of hybrid systems past hytech. In: International workshop on hybrid systems: computation and control, pp 258–273
Jiang S, Kumar R (2002) Failure diagnosis of discrete event systems with linear-time temporal logic fault specificatioans. In: Proc 2002 Amer control conf, pp 128–133
Jiang S, Kumar R, Garcia H (2002) Diagnosis of repeated failures in discrete event systems. In: Proc 41st IEEE conf decision and control, pp 4000–4005
Kupferman O, Vardi YM (1996) Verification of fair transition systems. In: International conference on computer aided verification, pp 372–382
Lafortune S, Teneketzis D, Sampath M, Sengupta R, Sinnamohideen K (2001) Failure diagnosis of dynamic systems: an approach based on discrete event systems. In: Amer control conf, pp 2058–2071
Lamperti G, Zanella M (1999) Diagnosis of discrete event systems integrating synchronous and asynchronous behvior. In: 9th int workshop on principles of diagnosis, pp 129–139
Lin F (1994) Diagnosability of discrete event systems and its application. Discrete Event Dyn Syst Theory Appl 4(2):197–212
Lunze J (1994) Qualitative modelling of linear dynamical systems with quantized state measurements. Automatica 30:417–431
Lunze J, Nixdorf B, Schroder J (1999) Deterministic discrete-event representations of linear continuous-variable systems. Automatica 35:395–406
Manna Z, Pnueli A (1992) The temporal logic of reactive and concurrent systems: specification. Springer, Berlin
Nuutila E, Soisalon-Soininen E (1994) On finding the strongly connected components in a directed graph. Inf Process Lett 49:9–14
Pandalai D, Holloway L (2000) Template languages for fault monitoring of discrete event processes. IEEE Trans Autom Control 45(5):868–882
Provan G, Chen Y-L (1998) Diagnosis of timed discrete event systems using temporal causal networks: modeling and analysis. In: Int workshop on discrete event systems, pp 152–154
Sampath M, Lafortune S, Teneketzis D (1998) Active diagnosis of discrete-event systems. IEEE Trans Autom Control 43(7):908–929
Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis DC (1995) Diagnosability of discrete-event systems. IEEE Trans Autom Control 40(9):1555–1575
Sampath M, Sengupta R, Lafortune S, Sinnamohideen K, Teneketzis DC (1996) Failure diagnosis using discrete-event models. IEEE Trans Autom Control 4(2)105–124
Thorsley D, Teneketzis D (2005) Diagnosability of stochastic discrete-event systems. IEEE Trans Autom Control 50(4):476–492
Yoo T-S, Lafortune S (2002) Polynomial-time verification of diagnosability of partially observed discrete-event systems. IEEE Trans Autom Control 47(9):1491–1495
Zad SH, Kwong RH, Wonham WM (2003) Fault diagnosis in discrete-event systems: framework and model reduction. IEEE Trans Autom Control 48(7):1199–1212
Zad SH, Kwong RH, Wonham WM (2005) Fault diagnosis in discrete-event systems: incorporating timing information. IEEE Trans Autom Control 50(7):1010–1015
Acknowledgements
The would like to thank all the anonymous reviewers and associate editor for constructive suggestions that helped in improvement of the presentation.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Biswas, S., Sarkar, D., Mukhopadhyay, S. et al. Fairness of Transitions in Diagnosability of Discrete Event Systems. Discrete Event Dyn Syst 20, 349–376 (2010). https://doi.org/10.1007/s10626-009-0077-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10626-009-0077-4