e-journal
Polynomial Test for Stochastic Diagnosability of Discrete-Event Systems
Two types of diagnosability of stochastic discrete-event systems (DESs) were introduced by Thorsley et al.
in 2005, where a necessary and sufficient condition for Strong Stochastic (SS)-Diagnosability (referred as A-diagnosability by Thorsley and Teneketzis, 2005), and a sufficient condition for Stochastic (S)-Diagnosability (referred as AA-diagnosability by Thorsley and Teneketzis, 2005), both with exponential complexity, were reported. In this paper, we present polynomial complexity tests for checking: (i) necessity and sufficiency of SS-Diagnosability;(ii) sufficiency of S-Diagnosability; and (iii) sufficiency as well as necessity of S-Diagnosability; the latter requires an additional notion of probabilistic equivalence. Thus, the work presented improves the accuracy as well as the complexity of
verifying stochastic diagnosability. Note to Practitioners—Detecting system failures is essential
prior to any failure tolerance action. For stochastic discrete-event systems, the property of S-Diagnosability allows one to detect any system failure with arbitrarily small error bound and within
bounded delay. Thus, S-Diagnosability should first be assured to enable the design of online detection scheme. This paper contributes by reducing the complexity and increasing the accuracy of checking S-Diagnosability properties.
Index Terms—Complexity, discrete-event system (DES), hypothesis testing, Stochastic diagnosability.
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