State-Based Control of Fuzzy Discrete-Event Systems

To effectively represent possibility arising from states and dynamics of a system, fuzzy discrete-event systems (DESs) as a generalization of conventional DESs have been introduced recently. Supervisory-control theory based on event feedback has been well established for such systems. Noting that the system state description, from the viewpoint of specification, seems more convenient, we investigate the state-based control of fuzzy DESs in this paper. An approach to finding all fuzzy states that are reachable by controlling the system is presented first. After introducing the notion of controllability for fuzzy states, a necessary and sufficient condition for a set of fuzzy states to be controllable is then provided. It was also found that event- and state-based controls are not equivalent, and the relationship between them was further discussed. Finally, we examine the possibility of driving a fuzzy DES under control from a given initial state to a prescribed set of fuzzy states and then keeping it there indefinitely