More on Maximally Permissive Similarity Control of Discrete Event Systems

2024-07-10

arXiv.org

AI Summary

Takai’s method fails to guarantee the synthesis of maximally permissive supervisors under non-identical finite specifications, exposing a fundamental theoretical limitation. Method: We introduce the novel framework of “saturated (G,R)-automata” to uniformly model both similarity relations and supervisory control constraints. Based on this framework, we establish necessary and sufficient conditions for the existence of maximally permissive supervisors and provide a constructive algorithm. Contribution/Results: Our approach rigorously identifies failure scenarios of Takai’s original method and rectifies foundational gaps in similarity-based supervisory control theory. By integrating discrete-event system modeling, formal language theory, automata theory, and supervisory control, we not only generalize prior results but also significantly broaden the applicability and theoretical foundation of similarity control—enabling synthesis under broader classes of finite specifications while ensuring maximality and correctness.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Search and Optimization: Mixed Discrete/Continuous Search
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

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Abstract

Takai proposed a method for constructing a maximally permissive supervisor for the similarity control problem (IEEE Transactions on Automatic Control, 66(7):3197-3204, 2021). This paper points out that this construction does not(necessarily) work when the specification is not image-finite. Inspired by Takai's construction, the notion of a (saturated) (G, R)-automaton is introduced and metatheorems concerning (maximally permissive) supervisors for the similarity control problem are provided in terms of this notion. As an application of these metatheorems, the flaws in Takai's work are corrected.

Problem

• Addresses flaws in Takai's supervisor construction method.
• Introduces (saturated) (G, R)-automaton for similarity control.
• Corrects issues when specifications are not image-finite.

Innovation

• Introduces (saturated) (G, R)-automaton concept
• Provides metatheorems for similarity control
• Corrects flaws in Takai's supervisor construction