TY - JOUR

T1 - On the Existence of Finite State Supervisors for Arbitrary Supervisory Control Problems

AU - Sreenivas, Ramavarapu S.

N1 - Funding Information:
Manuscript received December 22, 1992; revised February 26, 1993. This work was supported in part by the UIUC Campus Research Board under Grant RES-BRD-IC-SREENIVAS-1-2-6831 7. The author is with the Department of General Engineering and the Co- ordinated Science Laboratories, University of Illinois at Urbana-Champaign, Urbana, IL 61801. IEEE Log Number 9216447.

PY - 1994/4

Y1 - 1994/4

N2 - Given two prefix closed languages K, L ⊆ Σ*, where K ⊆ ⊆ L represents the desired closed-loop behavior and L is the open-loop behavior, there exists a finite-state supervisor that enforces K in the closed loop if and only if there is a regular, prefix-closed language M ⊆ ⊆ Σ*such that: 1) M Σu⊓ L ⊆ ⊆ M, and 2) M ⊓ L = K (cf. [9] for an equivalent definition). In this paper, we_show that this is equivalent to: 1) the controllability of sup{P ⊆ ⊆ K ∪ L | pr(P) = P} with respect to Σ*, and 2) the regularity of sup{P ⊆ ⊆ K ∪ | pr(P) = P}, where L = Σ*— L and pr(•) is the set of prefixes of strings in the language argument. We use this property to investigate the issue of deciding the existence of a finite-state supervisor for different representations. We also present some properties of the language sup{P ⊆ ⊆ K ∪ L | pr(P) = P}, along with implications to the synthesis of solutions to the supervisory control problem with the fewest states.

AB - Given two prefix closed languages K, L ⊆ Σ*, where K ⊆ ⊆ L represents the desired closed-loop behavior and L is the open-loop behavior, there exists a finite-state supervisor that enforces K in the closed loop if and only if there is a regular, prefix-closed language M ⊆ ⊆ Σ*such that: 1) M Σu⊓ L ⊆ ⊆ M, and 2) M ⊓ L = K (cf. [9] for an equivalent definition). In this paper, we_show that this is equivalent to: 1) the controllability of sup{P ⊆ ⊆ K ∪ L | pr(P) = P} with respect to Σ*, and 2) the regularity of sup{P ⊆ ⊆ K ∪ | pr(P) = P}, where L = Σ*— L and pr(•) is the set of prefixes of strings in the language argument. We use this property to investigate the issue of deciding the existence of a finite-state supervisor for different representations. We also present some properties of the language sup{P ⊆ ⊆ K ∪ L | pr(P) = P}, along with implications to the synthesis of solutions to the supervisory control problem with the fewest states.

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U2 - 10.1109/9.286270

DO - 10.1109/9.286270

M3 - Article

AN - SCOPUS:0028419848

VL - 39

SP - 856

EP - 861

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

SN - 0018-9286

IS - 4

ER -