Diagnosability of stochastic discrete-event systems

Abstract

Abstract-We investigate diagnosability of stochastic discrete-event systems. We define the notions of A-and AA-diagnosability for stochastic automata; these notions are weaker than the corresponding notion of diagnosability for logical automata introduced by Sampath et al. Through the construction of a stochastic diagnoser, we determine offline conditions necessary and sufficient to guarantee A-diagnosability and sufficient to guarantee AA-diagnosability. We also show how the stochastic diagnoser can be used for on-line diagnosis of failure events. We illustrate the results through two examples from HVAC systems.Index Terms-Discrete-event systems, failure detection, fault diagnosis, probabilistic models, stochastic automata.

Stochastic event counter for discrete-event systems under unreliable observations

“…Email: {Tae-Sic.Yoo, Humberto.Garcia}@inl.gov 1 The stochastic diagnoser is not a stochastic automaton. Therefore, the results presented in [6], [9] do not contradict each other.…”

“…These notions of diagnosability relax that of deterministic automaton introduced in [8]. Also presented in [9] is the procedure of building the stochastic diagnoser 1 that bears a similar structure of the logical diagnoser of [8]. The transitions of the stochastic diagnoser include probability transition matrixes that can be used to update the probability distribution on the state estimate.…”

“…Among the subsequent extensions and improvements of [8], recent developments on the detection problem of special events accounting for sensor unreliability and stochastic aspects in discrete-event systems include [6], [9], [1]. In [6], the authors show that, in general, the observer of a finite-state stochastic automaton cannot be represented by another finite-state stochastic automaton.…”

“…In [6], the authors show that, in general, the observer of a finite-state stochastic automaton cannot be represented by another finite-state stochastic automaton. In [9], the authors introduced the notions of stochastic diagnosability that incorporate the stochastic automaton describing the behavior of the system. These notions of diagnosability relax that of deterministic automaton introduced in [8].…”

Lyapunov Stability of Fuzzy Discrete Event Systems

“…It is well known that the issues of diagnosability for DESs are of practical and theoretical importance, and have received extensive attention in recent years [5][6][7][8][9]12,13,[15][16][17][23][24][25][26][27][29][30][31][32][33][34][35][36][37][38][39]. However, the observability and the failure set of events in the literature are usually crisp.…”