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Control of Parameterized Discrete Event Systems

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Abstract

This paper investigates the control of parameterized discrete event systems when specifications are given in terms of predicates and satisfy a similarity assumption. This study is motivated by a weakness in current synthesis methods that do not scale well to huge systems. For systems consisting of similar processes under total or partial observation, conditions are given to deduce properties of a system of n processes (arbitrary size) from properties of a system of n 0 processes (bounded size), with n ≥ n 0. Furthermore, it is shown how to infer a control policy for the former from the latter’s, while taking into account interconnections between processes.

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Notes

  1. Quantifications have the form (quantifier bound variable | range restriction : quantified expression) (see, e.g., Gries and Schneider 1995); an empty range in a quantification means that the bound variable ranges over all possible values. \((\exists x\mid P : Q)\) is read as “there exists x such that P and Q”. ( ∀ x|P : Q) is read as “for all x such that P, Q holds” or as “for all x, P implies Q”.

  2. In several examples, the abbreviation A i is used for x[i] = A i , where A i  ∈ X i .

  3. i ⊕ 1 equals 1 if i = n, and i + 1 otherwise.

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Acknowledgements

The research described in this paper was supported in part by the Natural Sciences and Engineering Research Council of Canada. The authors would like to thank Michel Embe Jiague for his suggestion about Proposition 4.

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Authors and Affiliations

  1. xtranormal Inc., 5555, avenue Casgrain, 2e étage, H2T 1Y1, Montréal, Québec, Canada

    Hans Bherer

  2. Département d’informatique et de génie logiciel, Université Laval, Pavillon Adrien-Pouliot, 1065, avenue de la Médecine, G1V 0A6, Québec, Québec, Canada

    Jules Desharnais

  3. Département d’informatique, Université de Sherbrooke, 2500, boulevard de l’Université, J1K 2R1, Sherbrooke, Québec, Canada

    Richard St-Denis

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  1. Hans Bherer
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Correspondence to Richard St-Denis.

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Bherer, H., Desharnais, J. & St-Denis, R. Control of Parameterized Discrete Event Systems. Discrete Event Dyn Syst 19, 213–265 (2009). https://doi.org/10.1007/s10626-008-0040-9

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