对称离散事件系统事件重标记观测器性质研究

Study on relabeling observer property in symmetric discrete-event systems

当离散事件系统(discrete-event systems,DES)由多组结构相同的组件构成时,则称离散事件系统具有对称性.为了化简对称离散事件系统的状态空间,本文提出事件重标记映射,将完成相同任务的事件标记为同一事件,将与控制无关的不可控事件设为不可观测事件,并将其标记为空字符擦除.为了确保事件重标记前后系统对应的最大监督控制器具有相同的控制效果,本文引入重标记观测器(relabeling observer property,ROP)的概念并给出判断被控对象对应的语言关于事件重标记映射是否具有重标记观测器性质的算法;然后运用重标记观测器性质证明事件重标记前后监督控制器控制效果的等价性,从而可用简化后的监督控制器实现与事件重标记操作前相同的控制任务.最后通过实例验证所提理论的正确性.

Symmetry arises when discrete-event systems(DES) consist of groups of identical components. To reduce the state space of symmetric DES, the event relabeling map is proposed in this paper. The event relabeling map relabels all events fulfilling the same task to one symbol and treats uncontrollable events irrelevant to control as unobservable events.Then the unobservable events are erased by relabeling them to the empty symbol. To ensure that the supremal controller remains control-equivalent after relabeling, the concept of relabeling observer property(ROP) is proposed, as well as steps to determine whether certain languages have this property. Based on the ROP, we show that the original supervisor and its relabeled counterpart are equivalent in control action. Namely, the reduced supervisor in the relabeled system achieves the same control goal as the supervisor in the original system before relabeling. Finally, examples are given to illustrate the validity of the proposed approach.