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A necessary and sufficient condition for diagnosability of stochastic discrete event systems

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Abstract

Stochastic discrete event systems (SDES) are systems whose evolution is described by the occurrence of a sequence of events, where each event has a defined probability of occurring from each state. The diagnosability problem for SDES is the problem of determining the conditions under which occurrences of a fault can be detected in finite time with arbitrarily high probability. (IEEE Trans Autom Control 50(4):476–492 2005) proposed a class of SDES and proposed two definitions of stochastic diagnosability for SDES called A- and A A-diagnosability and reported a necessary and sufficient condition for A-diagnosability, but only a sufficient condition for A A-diagnosability. In this paper, we provide a condition that is both necessary and sufficient for determining whether or not an SDES is A A-diagnosable. We also show that verification of A A-diagnosability is equivalent to verification of the termination of the cumulative sum (CUSUM) procedure for hidden Markov models, and that, for a specific class of SDES called fault-immediate systems, the sequential probability ratio test (SPRT) minimizes the expected number of observable events required to distinguish between the normal and faulty modes.

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  1. David Thorsley

    Present address: Quantcast Corporation, 795 Folsom Street, San Francisco, CA, USA

Authors and Affiliations

  1. Department of Electrical Engineering, University of Washington, Seattle, WA, USA

    David Thorsley

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  1. David Thorsley
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Correspondence to David Thorsley.

Additional information

This research is partially supported by NSF award #10002220, “Estimation and Observation of Stochastic Biochemical Networks.”

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Thorsley, D. A necessary and sufficient condition for diagnosability of stochastic discrete event systems. Discrete Event Dyn Syst 27, 481–500 (2017). https://doi.org/10.1007/s10626-017-0236-y

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  • DOI: https://doi.org/10.1007/s10626-017-0236-y

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