### Abstract

Consider an event alphabet Σ. The supervisory control theory of Ramadge and Wonham asks the question: given a plant model G with language L_{M}(G) ⊆ Σ* and another language K ⊆ L_{M}( G), is there a supervisor such that L_{M} (/G) = K? Ramadge and Wonham showed that a necessary condition for this to be true is the so-called controllability of with respect to L_{m} (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 sublanguage_{C} ⊆ (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 language | English (US) |
---|---|

Pages (from-to) | 826-829 |

Number of pages | 4 |

Journal | IEEE Transactions on Automatic Control |

Volume | 53 |

Issue number | 3 |

DOIs | |

State | Published - Apr 1 2008 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

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

### Cite this

}

**A note on the properties of the supremal controllable sublanguage in pushdown systems.** / Griffin, Christopher.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A note on the properties of the supremal controllable sublanguage in pushdown systems

AU - Griffin, Christopher

PY - 2008/4/1

Y1 - 2008/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=42649125282&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42649125282&partnerID=8YFLogxK

U2 - 10.1109/TAC.2008.919519

DO - 10.1109/TAC.2008.919519

M3 - Article

AN - SCOPUS:42649125282

VL - 53

SP - 826

EP - 829

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 3

ER -