Bisimilarity enforcing supervisory control for deterministic specifications

Abstract

This paper investigates the supervisory control of nondeterministic discrete event systems to enforce bisimilarity with respect to deterministic specifications. A notion of synchronous simulation-based controllability is introduced as a necessary and sufficient condition for the existence of a bisimilarity enforcing supervisor, and a polynomial algorithm is developed to verify such a condition. When the existence condition holds, a supervisor achieving bisimulation equivalence is constructed. Furthermore, when the existence condition does not hold, two different methods are provided for synthesizing maximal permissive sub-specifications.

School of Teacher, Nanjing Xiao Zhuang University, Nanjing, 210000, China

“…In the supervisory control theory [1,3,6,7,8,10,11], the events are divided into two classes: controllable and uncontrollable events. We denote by Σ uc (or, Σ c ) the set of uncontrollable (controllable, resp.)…”

“…The supervisory control theory, originating from the work of Ramadge and Wonham [1], provides a framework for control of discrete event systems. In this theory [1,2,3,4,5,6,7,8,9,10,11], both plants and specifications are modeled as (non)deterministic automata. A supervisor controller, called supervisor, is also modeled as an automaton, which exerts control over a plant such that the supervised system runs as desired.…”

“…In the development of supervisory control theory, various notions (e.g. language equivalence [1], bisimulation [7,11] and simulation [3,4,5,6,8,9,10]) have been adopted to formalize what it means that the behavior of a supervised system meets the requirements specified by a specification. Among them, the notion of simulation is suitable for handing situations with nondeterministic transitions and uncontrollable events.…”