A Note on the Proper ties of the Supremal Controllable Sublanguage in Pushdown Systems.

Journal Article · Mon Dec 31 23:00:00 EST 2007 · IEEE Transactions on Automatic Control

DOI:https://doi.org/10.1109/TAC.2008.919519· OSTI ID:939933

Griffin, Christopher H ^[1]

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1. ORNL

Consider an event alphabet $$\Sigma$$. The Supervisory Control Theory of Ramadge and Wonham asks the question, given a plant model $$G$$ with language $$\LanM(G) \subseteq \Sigma^{*}$$ and another language $$K \subseteq \LanM(G)$$, is there a supervisor $$\varphi$$ such that $$\LanM(\varphi/G)=K$$? Ramadge and Wonham showed that a necessary condition for this to be true is the so called \textit{controllability} of $$K$$ with respect to $$\LanM(G)$$. 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 \textit{supremal controllable sublanguage} $$\supC(K) \subseteq K$ that is is effectively constructable from generators of $$K$$ and $$G$$. In this paper, we show: (i) There is an algorithm to compute the supremal controllable sublanguage of a prefix closed $$K$$ accepted by a deterministic pushdown automaton when the plant language is also prefix closed and accepted by a finite state automaton. (ii) In this case, we show this supremal controllable sublanguage is also accepted by a DPDA.

• Research Organization: Oak Ridge National Laboratory (ORNL)
• Sponsoring Organization: ORNL other overhead
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 939933
• Journal Information: IEEE Transactions on Automatic Control, Journal Name: IEEE Transactions on Automatic Control Journal Issue: 3 Vol. 53
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
ALGORITHMS
Algorithm
CONTROL THEORY
Discrete Event Control
MACHINERY
Pushdown machine
Supremal Controllable Sublanguage