Simultaneous Reduction of Petri Nets and Linear Constraints for Efficient Supervisor Synthesis

Due to state-space explosion and uncontrollable events in discrete-event systems, it is very difficult to design supervisors to enforce user-defined linear-constraints and ensure the liveness of their Petri-net (PN) models with complex structures. Different from all the existing methods, which are to transform original constraints into admissible or weakly admissible ones, the method proposed in this work aims to reduce linear-constraints and PN models simultaneously. As a result, an original PN control problem is equivalently reduced to a simpler one, i.e., the optimal supervisors for them make the same restriction on the behavior of a discrete-event system. Moreover, it can be guaranteed that the original PN system is live if and only if the reduced one is so. Since the state space of a PN may grow exponentially with its size, and the sizes of real discrete-event systems are often too large to handle, the proposed method is useful to greatly reduce the computational complexity of both property-analysis and supervisor-synthesis of discrete-event systems.