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Computation of minimal event bases that ensure diagnosability

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Abstract

We deal with the problem of finding sets of observable events (event bases) that ensure language diagnosability of discrete-event systems modeled by finite state automata. We propose a methodology to obtain such event bases by exploiting the structure of the diagnoser automaton, and in particular of its indeterminate cycles. We use partial diagnosers, test diagnosers, and other new constructs to develop rules that guide the update of the observable event set towards achieving diagnosability. The contribution of this paper is the description of such rules and their integration into a set of algorithms that output minimal diagnosis bases.

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Notes

  1. Strictly speaking, the graph to be built in Algorithm 1 is not a rooted tree since distinct nodes may have the same label. The main reason for labeling two distinct nodes with the same label is due to the fact that we are unfolding a directed graph (diagnoser), which has cycles and, in some cases, there is more than one path from an origin state to a certain state.

  2. We point out that practical applications with real systems have yielded diagnosers whose state spaces are of the same order as those of the systems; see e.g. Sampath (2001), Sengupta (2001) and Sinnamohideen (2001). In these applications, the worst-case exponential upper bound is far from being attained due to the underlying system structure.

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Acknowledgements

We would like to thank the anonymous reviewers for their comments and suggestions which helped improve the presentation and readability of the paper. The research work of João Carlos Basilio has been supported by the Brazilian Research Council (CNPq), grants 200820/ 2006-0 and 307939/2007-3. The research of Stéphane Lafortune has been supported in part by NSF grants ECCS-0624821 and CNS-0930081.

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Authors and Affiliations

  1. COPPE, Programa de Engenharia Elétrica, Universidade Federal do Rio de Janeiro, 21949-900, Rio de Janeiro, R.J, Brazil

    João Carlos Basilio, Saulo Telles Souza Lima & Marcos Vicente Moreira

  2. Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI, 48109, USA

    Stéphane Lafortune

Authors
  1. João Carlos Basilio
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  2. Saulo Telles Souza Lima
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  3. Stéphane Lafortune
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  4. Marcos Vicente Moreira
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Corresponding author

Correspondence to João Carlos Basilio.

Appendix

Appendix

We present here two tables: Table 1 lists all the acronyms and Table 2 presents the main notation used in the paper.

Table 1 List of acronyms
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Table 2 Notation
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Basilio, J.C., Lima, S.T.S., Lafortune, S. et al. Computation of minimal event bases that ensure diagnosability. Discrete Event Dyn Syst 22, 249–292 (2012). https://doi.org/10.1007/s10626-012-0129-z

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  • DOI: https://doi.org/10.1007/s10626-012-0129-z

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