Diagnosability of a class of discrete event systems based on observations

The diagnosability of discrete event systems has been a topic of interest to many researchers. The diagnosability conditions for various systems have evolved based on a regularity condition that is imposed on faulty traces with respect to their observable continuations. Improving upon this weak but necessary condition, a new model of diagnosability that is based on sensor outputs, which are called observations, upon a command input is proposed in this paper. Necessary and sufficient conditions are derived for the proposed diagnosability model. The search performance of the proposed diagnosability condition is of linear complexity in terms of the power set of the system events and observations, compared to the exponential complexity of the search with the existing diagnosability regularity condition. Moreover, a system that is not diagnosable according to the existing diagnosability condition may be diagnosable in the proposed diagnosability model, which includes observations.