Diagnosability Analysis of Labeled Time Petri Net Systems

In this paper, we focus on two notions of diagnosability for labeled Time Petri net (PN) systems: <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula>-diagnosability implies that any fault occurrence can be detected after at most <inline-formula><tex-math notation="LaTeX">$K$</tex-math></inline-formula> observations, while <inline-formula><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula>-diagnosability implies that any fault occurrence can be detected after at most <inline-formula><tex-math notation="LaTeX">$\tau$</tex-math></inline-formula> time units. A procedure to analyze such properties is provided. The proposed approach uses the Modified State Class Graph, a graph the authors recently introduced for the marking estimation of labeled Time PN systems, which provides an exhaustive description of the system behavior. A preliminary diagnosabilty analysis of the underlying logic system based on classical approaches taken from the literature is required. Then, the solution of some linear programming problems should be performed to take into account the timing constraints associated with transitions.

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