Combining Online Diagnosis and Prognosis for Safe Controllability

In this article, we combine fault diagnosis and prognosis to generalize the notion of safe controllability of discrete-event systems. To do so, we reformulate the notions of safe diagnosability, prognosability, safe controllability by diagnosis, and safe controllability by prognosis in the context of strings. Moreover, we combine these notions to introduce the concept of safe controllability by diagnosis or prognosis, or simply DP-safe controllability. We show that a language can be DP-safe controllable even if it is not safe controllable either only by diagnosis or only by prognosis. Thus, the DP-safe controllability can be considered a generalization of the safe controllability concept found in the literature. If a DES is DP-safe controllable, to achieve fault tolerance using an active approach, reconfiguration actions could be forced based not only on online fault diagnosis, but also on online fault prognosis. Thus, our approach outperforms the previous ones, since it provides additional control options to keep the system away from forbidden zones and to switch from the nominal supervisor to a postfault-detection supervisor designed to achieve postfault performance objectives. Necessary and sufficient conditions for DP-safe controllability are presented and an example is used to illustrate the introduced concepts.