Residuation of tropical series: rationality issues

Eric Badouel 1 Anne Bouillard 2, 3 Philippe Darondeau 1 Jan Komenda 4
1 S4 - System synthesis and supervision, scenarios
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
3 TREC - Theory of networks and communications
DI-ENS - Département d'informatique de l'École normale supérieure, Inria Paris-Rocquencourt
Abstract : Decidability of existence, rationality of delay controllers and robust delay controllers are investigated for systems with time weights in the tropical and interval semirings. Depending on the (max,+) or (min,+)-rationality of the series specifying the controlled system and the control objective, cases are identified where the controller series defined by residuation is rational, and when it is positive (i.e., when delay control is feasible). When the control objective is specified by a tolerance, i.e. by two bounding rational series, a nice case is identified in which the controller series is of the same rational type as the system specification series.
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Submitted on : Monday, February 21, 2011 - 10:33:53 AM
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Eric Badouel, Anne Bouillard, Philippe Darondeau, Jan Komenda. Residuation of tropical series: rationality issues. [Research Report] RR-7547, INRIA. 2011, pp.19. ⟨inria-00567390⟩



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