Counterexample-Guided Abstraction-Refinement for Hybrid Systems Diagnosability Analysis

Abstract

Verifying behavioral or safety properties of hybrid systems, either at design stage such as state reachability and diagnosability, or on-line such as fault detection and isolation is a challenging task. We are concerned here with abstractions oriented towards hybrid systems diagnosability checking. The verification can be done on the abstraction by classical methods developed for discrete event systems extended with time constraints, which provide a counterexample in case of non-diagnosability. The absence of such a counterexample proves the diagnosability of the original hybrid system. In the presence of a counterexample, the first step is to check if it is not a spurious effect of the abstraction and actually exists for the hybrid system, witnessing thus non-diagnosability. Otherwise, we show how to refine the abstraction, guided by the elimination of the counterexample, and continue the process of looking for another counterexample until either a final result is obtained or we reach an inconclusive verdict. We make use of qualitative modeling and reasoning to compute discrete abstractions. Abstractions as timed automata are particularly studied as they allow one to handle time constraints that can be captured at a qualitative level from the hybrid system.

overview on diagnosability and prognosability for system monitoring

“…In (Zanella, 2017), || //l -diagnosability is presented to take into account temporal uncertainty into the diagnosability def-System Type Articles DES (Sampath, Sengupta, & Lafortune, 1995) and (Ye, Dague, & He, 2019) [Automata] (Zanella, 2017) [Twin plant : finite automata] (Basile, Chiacchio, & De Tommasi, 2012) [Labelled Petri Nets] (Yoo & Lafortune, 2002) [Finite-state automaton] (Madalinski, Nouioua, & Dague, 2010) [Labelled Petri Nets] CS (Staroswiecki & Comtet-Varga, 2001) [algebraic dynamic systems] (Zuniga, Sotomayor-Moriano, Chanthery, Travé-Massuyès, & Soto, 2019) (Cordier, Travé-Massuyes, Pucel, et al, 2006) HS (Zaatiti, Ye, Dague, & Gallois, 2017) [Partially observed hybrid automata] (Bayoudh & Travé-Massuyès, 2014) (Fourlas, Kyriakopoulos, & Krikelis, 2002) [Hybrid I/O Automata] HtS (Hsieh & Chen, 2008) [distributed] (Hua, Li, Ren, & Liu, 2016) Table 1. Reviewed articles on diagnosability classified by system types inition for systems modeled by automata.…”

“…The diagnosability in Partially Observable Hybrid Automaton (POHA), in which some variables are not observed, is defined in (Zaatiti et al, 2017) as follows.…”

“…Results of the diagnosability analysis Articles Diagnosable or not (Sampath et al, 1995) (Ye et al, 2019) (Bayoudh & Travé-Massuyès, 2014) (Staroswiecki & Comtet-Varga, 2001) (Yoo & Lafortune, 2002) (Madalinski et al, 2010) (Fourlas et al, 2002) Parameter Dependent (Zanella, 2017) [Dependent on temporal uncertainty window] (Basile et al, 2012) [Dependent on the number of transition] (Zaatiti et al, 2017) [Dependent on a given time] (Hsieh & Chen, 2008) [Dependent on number of detectable faulty components] Real number (Hua et al, 2016) Table 2. Reviewed articles on diagnosability classified by the type of result given by the diagnosability analysis Uncertainty Articles Temporal uncertainty (Zanella, 2017) Noise (Bayoudh & Travé-Massuyès, 2014) (Staroswiecki & Comtet-Varga, 2001) Node reliability (Hsieh & Chen, 2008) Table 3.…”

“…Definition 31 (S m -prognosability) S m -Prognosability means that for any threshold value ρ > 0 ∈ R and error bound τ > 0 ∈ R, there exists a reaction bound k ≥ m, such that if a fault f ∈ Σ f cannot be pre- (Bayoudh & Travé-Massuyès, 2014) [For the HS underlying DES] Time (Zaatiti et al, 2017) (Bayoudh & Travé-Massuyès, 2014) (Staroswiecki & Comtet-Varga, 2001) Can be done online (Hua et al, 2016) Table 4. Reviewed articles on diagnosability classified by the way to express time during the diagnosability analysis dicted k steps (i.e.…”