Recoverability of faulty discrete event systems

Here we discussed recoverability of faulty discrete event systems. A faulty discrete event system includes the healthy dynamics and the faulty dynamics. In faulty modes, the performance of the system often degrades. Hence we need to execute some recovery actions to recover the performance of the system. Recovery actions may be renewing/repairing the faulty device or re-configuring the healthy devices. Generally recovery actions can be fired not for all the time, but for some time. They were modeled as a mapping from the state set of the faulty mode to a binary set in which 1 means recovery actions can be fired and 0 means recovery actions cannot be fired. Then we defined two types of recoverabilities: recoverability and weak recoverability. Recoverability means we periodically have chances to do recovery actions and weak recoverability means we have at least one chance to do recovery actions when the system has a fault. With observer technology, we proposed criteria to check these two types of recoverabilities.