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Contributions à la commande des systèmes (max,+)-linéaires. Applications aux réseaux de transport.

Abstract : The functioning of Discrete event dynamic systems subject to synchronization and delay phenomena can be described by linear models in a particular algebraic structure called (max,+) algebra. A linear system theory has been developed over dioids (such as (max,+) algebra) by analogy with the conventional one. This report is devoted to control problem of (max,+)-linear systems. Some control problems for these systems have previously been tackled. In all these works, the problematic was to compute an optimal solution in regards of the just-in-time criterion while considering control objective such as reference model or reference output. For our concern, the first contribution to the control aim at delaying as less as possible the controlled system while ensuring some given specifications. More precisely, we consider specifications which fit on system state inequalities. Then, we study a new control criterion. We are interested in controller synthesis which delay as less as possible the system while ensuring a control objective defined by constraints on system state. Transportation networks can be described by a linear representation in (max,+)-algebra. The last part of this report is devoted to their study. We propose some tools for the evaluation performance and the control of these systems. Notably, the timetables synthesis problem is formulated and solved as (max,+)-linear system control.
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Contributor : Laurent Houssin <>
Submitted on : Friday, April 27, 2007 - 3:54:49 PM
Last modification on : Friday, May 21, 2021 - 12:04:01 AM
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  • HAL Id : tel-00143884, version 1


Laurent Houssin. Contributions à la commande des systèmes (max,+)-linéaires. Applications aux réseaux de transport.. Automatique / Robotique. Université d'Angers, 2006. Français. ⟨tel-00143884⟩



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