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Mutual exclusion problems widely exist in discrete event systems in which several processes will compete for the common resource for maintaining their normal running. This competition is mutually exclusive. However, a special behavior, that is, periodic mutual exclusion behavior, is important for many discrete event systems. Once a process obtains the common resource, it will consecutively obtain the common resource in the following several competitions. The other processes should wait for the release of the common resource. All processes will compete for the common resource again after the common resource is released. These competitions have obvious periodicity. In this paper, a methodology is proposed to design periodic mutual exclusion supervisors to control the periodic mutual exclusion behavior in discrete event systems. Moreover, two original structural conversion concepts, called k-derivation and k-convergence processes, are proposed to construct the periodic mutual exclusion supervisors. The discussion results show that many undesirable execution sequences are forbidden since the periodic mutual exclusion behavior is controlled by the proposed periodic mutual exclusion supervisors. Finally, an example is used to illustrate the proposed methodology

An Enhanced Supervisory Control Strategy for Periodicity Mutual Exclusions in Discrete Event Systems Based on Petri Nets