Modular Supervisory Control and Hierarchical Supervisory Control of Fuzzy Discrete-Event Systems

This paper establishes modular and hierarchical supervisory control theories of Fuzzy Discrete-Event Systems (FDES). It aims to resolve the horizontal and vertical complexities present in large-scale event-driven systems, which are affected by uncertainties in their event and state representations. The modular supervisory control architecture composed of a set of noncommunicating local supervisors, in which one supervisor is assigned for each module having its own sensing and acting capabilities. The notion of separability for languages in FDES is introduced and the property of a language specification of FDES, termed as separably-controllable-observability, is proposed to determine the existence of modular supervisors to the control problem. The hierarchical supervisory control architecture consists of multilevel supervisors assigned to detailed low-level and abstract high-level models of the plant. The notion of output-control-consistency is introduced for languages in FDES. Then, the property called strictly-output-control-consistency is defined for FDES in order to maintain the hierarchical consistency between low-level and high-level FDES modules. The property of H-fuzzy observability is introduced to ensure the hierarchical consistency under the partial observation of low-level FDES. Finally, using the established hierarchical supervisory control theory of FDES, a behavior-based mobile robot navigation example is discussed. Note to Practitioners-The modular and hierarchical supervisory control problems are studied for a class of complex and large-scale event-driven systems, that inherits state and event uncertainties. Examples of such systems include robotic systems, determining treatment regimens in drug delivery, chemical process automations, etc. Since, the information receives from these systems is subjected to uncertainties and noise, the crisp discrete modeling fails to perform well. Therefore, FDES, which incorporate fuzzy logics with Discrete-Event Systems (DES), is considered.