1Designs of Bisimilar Petri Net Controllers with Fault Tolerance Capabilities

In this paper we describe an approach for providing tolerance against faults that may compromise the functionality of a given controller that is modeled by a Petri net. Our method is based on embedding the given Petri net controller into a larger (redundant) Petri net controller that retains the original functionality and properties, and uses additional places, connections and tokens to impose invariant conditions that allow the systematic detection and identification of faults via linear parity checks. We discuss two types of redundant Petri net controllers: (i) non-separate redundant Petri net controllers have the same functionality as the given Petri net controller and allow us to perform fault detection and identification, but do not necessarily retain the given controller intact, and; (ii) separate redundant Petri net controllers are a special case of the non-separate redundant controllers that retain the given Petri net controller intact and use additional places to enable fault detection and identification. We obtain complete characterizations of both types of redundant controllers along with necessary and sufficient conditions for them to be bisimulation equivalent to the given, original Petri net controller. We also discuss how each type of redundant controllers can be designed to have desirable fault detection and identification capabilities. When the bisimulation equivalence requirement is not directly enforced, th