This paper is a survey of the history of max-plus algebra and its role in the field of discrete event systems during the last three decades. It is based on the perspective of the authors but it ...covers a large variety of topics, where max-plus algebra plays a key role.
This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the ...Petri net literature. These models do not admit a linear representation in (min, +) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model.
We deal with timed event graphs whose holding times associated with places are variable. Defining a first-in-first-out functioning rule, we show that such graphs can be linearly described in (max,+) ...algebra. Moreover, this linear representation allows extending the just-in-time control synthesis existing for timed event graphs with constant holding times. An example is proposed in order to illustrate how the approach can be applied as a just-in-time strategy for production lines.
A linear system theory has been developed for the class of discrete-event systems subject to synchronization. This paper presents the just-in-time control of such systems when reference input is ...updated and/or in the presence of uncontrollable input(s), the proposed controls are the solutions to an optimization problem under equality constraint.
This paper deals with feedback controller synthesis for timed event graphs in dioids. We discuss here the existence and the computation of a controller which leads to a closed-loop system whose ...behavior is as close as possible to the one of a given reference model and which delays as much as possible the input of tokens inside the (controlled) system. The synthesis presented here is mainly based on residuation theory results and some Kleene star properties.
This paper deals with the synthesis of greatest linear causal feedback for discrete-event systems whose behavior is described in dioid. Such a feedback delays as far as possible the input of the ...system while keeping the same transfer relation between the input and the output. When a feedback exists in the system, the authors show how to compute a greater one without decreasing the system's performance.
This note proposes an internal model control for linear discrete-event systems over max-algebra. We concentrate on the controller block of this control structure.
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