Robustness of a class of controlled Petri nets

In our previous works, we have unveiled the fault tolerant properties of several subclasses of controlled Petri nets, including CPPN, MG-refined nets and CAPN. In this paper, we extend the results to a class of controlled Petri net with uncertainties and flexible routes (CPNU-FR). By exploiting the routing flexibility of a CPNU-FR, we characterize a feasible condition to maintain production for a certain type of products by keeping the liveness of a cyclic production route. Based on this condition, we propose a structural decomposition method to test the feasibility of production routes. Based on the liveness condition for the nominal CPN, we characterize a condition to test whether a certain type of resource failures is tolerable.