TY - JOUR

T1 - On a Weaker Notion of Controllability of a Language K with respect to a Language L

AU - Sreenivas, Ramavarapu S.

N1 - Funding Information:
Using the decidability of weak controllability as the test for viability of modeling formalisms it was thought that weak controllability might result in a larger set of viable modeling formalisms as compared to those obtained for the usual definition Manuscript received April 17, 1992; revised June 5, 1992 and August 7, 1992. This work was supported in part by the National Science Foundation under Grant CDR-8803012, ECS-91-02346, in part by the Office of Naval Research Grants N00014-90-J-1093 and N00014-89-J-1023 and in part by the Army Grant DAAL-03-91-G-0194 and DAAL-03-86-K-0171. R. S. Sreenivas is with the Pierce Hall G12h, Division of Applied Sciences, Harvard University, Cambridge, MA 02138. IEEE Log Number 9208707.

PY - 1993/9

Y1 - 1993/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0027659816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027659816&partnerID=8YFLogxK

U2 - 10.1109/9.237665

DO - 10.1109/9.237665

M3 - Article

AN - SCOPUS:0027659816

SN - 0018-9286

VL - 38

SP - 1446

EP - 1447

JO - IRE Transactions on Automatic Control

JF - IRE Transactions on Automatic Control

IS - 9

ER -