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On the Computation of Natural Observers in Discrete-Event Systems

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Abstract

Natural projections with the observer property have proved effective in reducing the computational complexity of nonblocking supervisory control design, and the state sizes of the resulting controllers. In this paper we present an algorithm to verify this property, or if necessary to achieve it. A natural projection is a special type of general causal reporter map; for the latter an algorithm is already known for verification and modification. This algorithm could be used to verify the observer property of a natural projection, but if the natural projection is not an observer the algorithm is not applicable to modify it to an observer. Also, while a general reporter map always admits a unique smallest refinement with the observer property, a natural projection does not. Indeed there may exist several minimal extensions to the original observable event set of a natural projection. We show that the problem of finding a minimal extension is NP-hard, but propose a polynomial-time algorithm that always finds an acceptable extension. While not guaranteed to be minimal, it is in practice often reasonably small.

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Notes

  1. This monograph was first available online in 1998 under the title Notes on Control of Discrete-Event Systems. Since then it has been annually updated. The title was changed to Supervisory Control of Discrete-Event Systems in 2004.

  2. If a natural projection of a DES does not satisfy the observer property, the projected model may be exponentially larger than the original (Wong 1998).

  3. Here the parallel with linear system theory is exact: cf. Wonham (1985), Section 3.2.

  4. Available on the website http://www.control.utoronto.ca/DES.

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Authors and Affiliations

  1. Embedded Control Systems Research Group, Department of Machine Design, KTH-Royal Institute of Technology, Stockholm, Sweden

    Lei Feng

  2. Systems Control Group, Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada

    W. M. Wonham

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  1. Lei Feng
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  2. W. M. Wonham
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Correspondence to Lei Feng.

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Feng, L., Wonham, W.M. On the Computation of Natural Observers in Discrete-Event Systems. Discrete Event Dyn Syst 20, 63–102 (2010). https://doi.org/10.1007/s10626-008-0054-3

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