On time diagnosis of discrete event systems

A formulation and solution methodology for on-time fault diagnosis in discrete event systems is presented. This formulation and solution methodology captures the timeliness aspect of fault diagnosis and is therefore different from all other approaches to fault diagnosis in discrete event systems which are asymptotic in nature. A monitor observes a projection of the events that occur in the system. After each observation it can either raise an alarm and shut down the system or allow the system to continue. If the system is stopped when no fault had occurred, a false alarm penalty is incurred; on the other hand if a fault had occurred, a delayed detection penalty is incurred. Both these penalties are trace dependent. The on-time diagnosis problem is formulated as a minimax optimization problem where the objective is to choose a monitoring rule which minimizes the worst case cost along all traces of the language describing the discrete event system. An optimal diagnosis rule is determined using a dynamic programming algorithm. An example is presented which illustrates our methodology and high lights the difference between our formulation of on-time diagnosis with existing results on asymptotic diagnosis of discrete event systems.