Nonblocking Distributed State-Tree-Structures

Abstract

Discrete-event systems encompass a wide variety of today’s systems including manufacturing cells and networking protocols. To prevent a system from entering a forbidden state and to ensure nonblockingness, it is desirable to control, or restrict, the behavior of such a system. The supervisory control paradigm allows for the synthesis of a supervisor which produces the necessary feedback to appropriately restrict the behavior of the system. When discrete-event systems are described modularly, the number of states grows exponentially with the number of components; this is known as the state-space explosion problem and is one of the central challenges of supervisory control. State-tree-structures and modular approaches are strategies which address issues of complexity in supervisory control. However, both still suffer from heavy computations when ensuring nonblockingness. In this thesis we introduce a novel procedure for a more efficient check for nonblockingness of state-tree-structures. This is accomplished using the structural properties of state-tree-structures to separate the shared events from the unshared events of a system. We build a recursive two-layer hierarchy in which the bottom level contains the parallel components, and the top level is an abstracted view containing the shared events between these components. To maintain reachability properties in the top level, the components of the system must be clustered such that in each cluster one can reach every outgoing transition from each incoming transition. This is formalized as a uni- versally reachable cluster. We introduce an algorithm which optimally clusters system components in such a manner. This clustering allows us to reformulate the conditions of nonblockingness in a hierarchical manner; the system is nonblocking if and only if both the top level and each component in the bottom level are nonblocking. Given a small top level and that the bottom level has no shared events, the components can be analyzed independently and in parallel, thus drastically reducing computation times. To verify performance, the universally reachable clustering algorithm was implemented and analyzed for a set of random automata and was found to reduce the number of states on average by 95%. Additionally, our entire procedure to verify nonblockingness was applied to a practical production cell example in which we achieved a 99.99% reduction in the number of states to be examined.Computer EngineeringSoftware TechnologyElectrical Engineering, Mathematics and Computer Scienc