Decomposition and localization of a supervisor are both reduction methods in distributed supervisory control of discrete-event systems. Decomposition is employed to reduce the number of events and localization is used to reduce the number of states of local controllers. In decomposition of a supervisor both observation and control scopes are restricted, whereas in localization only control authority is restricted to the corresponding local controller. In this paper, we propose a decomposition method by defining a coparanormality property, and by using the relative observability property of a monolithic supervisor. Coparanormality is a coobservation property defined based on a paranormality property for a set of natural projections. It is shown that each supervisor can be coparanormal, provided a set of appropriate natural projections exist. Moreover, it is proved that relative observability is a sufficient condition to decompose a supervisor. Furthermore, the supervisor localization procedure is generalized to find a set of local controllers for any partition of the controllable events set. The implementation of such local controllers may become easier in industrial systems.

中文翻译：

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离散事件系统分布式监督控制中的协同性

监督者的分解和定位都是离散事件系统分布式监督控制的约简方法。分解用于减少事件的数量，而本地化用于减少本地控制器的状态数量。在监督者分解中，观察和控制范围都受到限制，而在本地化中，只有控制权限被限制在相应的本地控制器。在本文中，我们提出了一种分解方法，它定义了一个共通性属性，并使用了整体监管者的相对可观察性属性。Coparanormality 是基于一组自然投影的超常性属性定义的 coobservation 属性。结果表明，如果存在一组适当的自然投影，则每个监督者都可以是超自然的。此外，证明了相对可观察性是分解监督者的充分条件。此外，监督者本地化过程被概括为为可控事件集的任何分区找到一组本地控制器。在工业系统中，这种本地控制器的实施可能会变得更容易。