Generalized Critical Observability of Labeled Petri Nets Under Nondeterministic Observations

This paper addresses the property of critical observability in labeled Petri nets. A system is deemed critically observable if its state estimate (formed by observing the system output) can be determined to belong to a set of either critical markings or non-critical markings. More generally, for a critically observable system, there may be multiple types of critical markings and the operator may desire to know the type to which the current state estimate belongs. We propose a generalized version of critical observability, namely generalized critical observability, and provide two necessary and sufficient conditions to check it based on basis markings and integer linear programs, effectively circumventing the need for an exhaustive enumeration of all reachable markings of the net. In addition, we investigate (generalized) critical observability of Petri nets under nondeterministic observations, which may arise due to the loss of transmission signals or due to interference with sensor measurement outputs. To handle this, an augmented system is constructed from the original Petri net by adding new transitions that capture the effect of transitions associated with nondeterministic labels. Thus, we transform the verification of (generalized) critical observability of a Petri net under nondeterministic observations to that of the augmented model. Two real-world examples illustrate the applicability of the presented notion and methodology.