Signed real measure of regular languages for discrete-event automata

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Abstract

This paper presents the concept and formulation of a signed real measure of regular languages for analysis of discrete-event supervisory control systems. The measure is constructed based upon the principles of language theory and real analysis for quantitative evaluation and comparison of the controlled behaviour for discrete-event automata. The marked (i.e. accepted) states of finite-state automata are classified in different categories such that the event strings terminating at good and bad marked states have positive and negative measures, respectively. In this setting, a controlled language attempts to disable as many bad strings as possible and as few good strings as possible. Different supervisors may achieve this goal in different ways and generate a partially ordered set of controlled languages. The language measure creates a total ordering on the performance of the controlled languages, which provides a precise quantitative comparison of the controlled plant behaviour under different supervisors. Total variation of the language measure serves as a metric for the space of sublanguages of the regular language.

Original languageEnglish (US)
Pages (from-to)1800-1808
Number of pages9
JournalInternational Journal of Control
Volume76
Issue number18
DOIs
StatePublished - Dec 15 2003

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications

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