A note on the properties of the supremal controllable sublanguage in pushdown systems

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Abstract

Consider an event alphabet Σ. The supervisory control theory of Ramadge and Wonham asks the question: given a plant model G with language LM(G) ⊆ Σ* and another language K ⊆ LM( G), is there a supervisor such that LM (/G) = K? Ramadge and Wonham showed that a necessary condition for this to be true is the so-called controllability of with respect to Lm (G). They showed that when G is a finite-state automaton and K is a regular language (also generated by a finite state automaton), then there is a regular supremal controllable sublanguageC ⊆ (K) that is effectively constructable from generators of K and G. In this paper, we show: 1) there is an algorithm to compute the supremal controllable sublanguage of a prefix closed K accepted by a deterministic pushdown automaton (DPDA) when the plant language is also prefix closed and accepted by a finite state automaton and 2) in this case, we show that this supremal controllable sublanguage is also accepted by a DPDA.

Original languageEnglish (US)
Pages (from-to)826-829
Number of pages4
JournalIEEE Transactions on Automatic Control
Volume53
Issue number3
DOIs
StatePublished - Apr 1 2008

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

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