Weak Diagnosability of Discrete-Event Systems

This article investigates weak diagnosability of discrete-event systems. Although diagnosability has been extensively investigated in the literature, weak diagnosability is a new concept introduced in this article. While diagnosability requires that a fault can be diagnosed along all trajectories after its occurrence, weak diagnosability requires that there always exists at least one trajectory along which the fault can be diagnosed at any time after its occurrence. Weak diagnosability ensures that any fault can be diagnosed eventually (with probability 1) but requires less sensors. We develop algorithms to check weak diagnosability. We further investigate weak diagnosability under communication delays and packet losses. We show that while packet losses may impact negatively on weak diagnosability, communication delays will not. We illustrate the results using a practical example.