### Abstract

A prefix-closed language K ⊆ Σ is said to be controllable with respect to another prefix-closed language L ⊆ Σ if and only if i) K ⊆ L, and ii) KΣu ∩ L [formula omitted] K, where [formula omitted] and [formula omitted] (cf. [6]). In this note, we consider a weaker notion of controllability where it is not required that K [formula omitted] L. If L is the prefix-closed language generated by a plant automaton G, then essentially there exists a supervisor [formula omitted] that is complete with respect to G such that [formula omitted]G) = K [formula omitted] L if and only if K is weakly controllable with respect to L (cf. [6, proposition 5.1]). For an arbitrary modeling formalism we show that the inclusion problem is reducible to the problem of deciding the weaker notion of controllability. Therefore, removing the requirement that K [formula omitted]L from the original definition of controllability does not help the situation from a decidability viewpoint. This observation is then used to identify modeling formalisms that are not viable for supervisory control of the untimed behaviors of discrete event dynamic systems.

Original language | English (US) |
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Pages (from-to) | 1446-1447 |

Number of pages | 2 |

Journal | IEEE Transactions on Automatic Control |

Volume | 38 |

Issue number | 9 |

DOIs | |

State | Published - Sep 1993 |

Externally published | Yes |

### ASJC Scopus subject areas

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