Brief paper: Formulae relating controllability, observability, and co-observability

Authors:
Ratnesh Kumar;Mark A. Shayman
Affiliations:
Department of Electrical Engineering, University of Kentucky, Lexington, KY 40506-0046, U.S.A.;Electrical Engineering Department and Institute for Systems Research, University of Maryland, College Park, MD 27042, U.S.A.
Venue:
Automatica (Journal of IFAC)
Year:
1998

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Abstract

We present formulae relating controllability, observability, and co-observability arising in the context of supervisory control of discrete event systems. Given a discrete event plant G with event set @e, uncontrollable event set @e"u"i, and observation mask M"i of the ith supervisor, we first show that the infimal prefix-closed, (L(G), @?"i @e"u"i)-controllable, and (L(G), @e"u"i, M"i)-co-observable superlanguage equals the intersection (taken over all i's) of the infimal prefix-closed, (L(G), @e"u"i)-controllable, and (L(G), M"i)-observable superlanguage. Next, we show that the infimal prefix-closed, and (@e^*, M)-observable superlanguage computation preserves (@e^*, @e"u)-controllability. These results can be used to compute individual supervisors in the decentralized control setting.