A Framework for Compositional Synthesis of Modular Nonblocking Supervisors

Abstract

This paper describes a framework for compositional supervisor synthesis, which is applicable to all discrete event systems modelled as a set of deterministic automata. Compositional synthesis exploits the modular structure of the input model, and therefore works best for models consisting of a large number of small automata. The state-space explosion is mitigated by the use of abstraction to simplify individual components, and the property of synthesis equivalence guarantees that the final synthesis result is the same as it would have been for the non-abstracted model. The paper describes synthesis equivalent abstractions and shows their use in an algorithm to efficiently compute supervisors. The algorithm has been implemented in the DES software tool Supremica and successfully computes nonblocking modular supervisors, even for systems with more than 10 14 reachable states, in less than 30 seconds.

An algorithm for compositional nonblocking verification using special events

“…It is likely that similar results can be obtained for compositional synthesis [42]. Furthermore, always enabled and selfloop-only events naturally arise from particular guard and update formulas of extended finite-state machines [31,43], so it is likely that they can help with the analysis of such systems as well.…”

Certainly Unsupervisable States

“…If a temporal logic specification is the conjunction of several requirements, it is possible to synthesise separate controller components for each requirement [5,7]. Compositional approaches in supervisory control [9,16] exploit the structure of the model of the plant to be controlled, which typically consists of several interacting components. These approaches avoid constructing the full state space by first simplifying individual components, then applying synchronous composition step by step, and simplifying the intermediate results again.…”

“…Supervision equivalence [9] and synthesis abstraction [16] have been proposed for this purpose, and several abstraction methods to simplify automata preserving these properties are known.…”

“…This paper proposes another abstraction method that can be used in compositional synthesis frameworks such as [9,16]. The proposed method finds all the states that will certainly be removed by any supervisor.…”

“…Section 2 introduces the terminology of supervisory control theory [21] and the framework of compositional synthesis [9,16]. Next, Section 3 explains the ideas of compositional synthesis with certainly unsupervisable states using the example of a manufacturing system.…”