Synthesis of greatest linear feedback for timed-event graphs in dioid

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\u27s performance

Max-Plus-Linear Systems for Modeling and Control of Manufacturing Problems

In this chapter, the dynamics of manufacturing systems is characterized through the occurrence of events such as parts entering or leaving machines. Furthermore, we assume that the relations between events are expressed by synchronizations (i.e., conditions of the form: for all k ≥ l, occurrence k of event e2 is at least τ units of time after occurrence k − l of event e1). Note that this assumption often holds when the considered manufacturing system is functioning under a predefined schedule. First, we discuss the modeling of such systems by linear state-space models in the (max,+)-algebra (due to this property, such systems are often called (max,+)-linear systems). Second, standard open-loop and closed-loop control structures for (max,+)-linear systems are recalled. These control structures lead to a trade-off between the rapidity of systems and their internal buffer sizes. Some techniques to influence this trade-off are presented

Heap Models, Composition and Control

International audienc

Control of Time-Constrained Dual-Armed Cluster Tools Using (max, +) Algebra

International audienceThe problem studied in this paper is the control of discrete event systems subject to strict temporal constraints using (max, +) algebra. Initially we sought necessary and sufficient conditions for the existence of a causal control law guaranteeing the respect of the temporal constraints. Subsequently, a method for calculating the control law, if any, is proposed. The application which we are interested in is the control of a manufacturing semiconductor wafers process subject to strict temporal constraints

Stabilising feedback in Max-Plus linear models of discrete processes

This article relates to a synthesising output feedback that is used to control a network of discrete events. The feedback stabilises the system without reducing its initial throughput and its synthesis is mainly based on the theory of residues and the Kleene operator. This article suggests some theoretical results and mathematical foundations of max-plus algebra theory, and in particularly, discusses various other aspects of controlling discrete processes and their modelling in the context of a linear max-plus system

On max-plus linear dynamical system theory: the observation problem

In this paper, we are interested in the general problem of estimating a linear function of the states for a given Max-Plus linear dynamical system. More precisely, using only the current and past inputs/outputs of the system, we want to construct a sequence that converges in a finite number of steps to the value given by a linear function of the states, for all initial conditions of the system. We provide necessary and sufficient conditions to solve this general problem. We also define and study a Max-Plus version of the well-known Luenberger observer, which is a subclass of the general problem that we are interested in, and we also provide necessary and sufficient conditions to solve this particular problem of observer synthesis. Finally, we show that there are important connections between results in the Max-Plus domain and associated results in the standard linear systems theory

Observer-Based Controller for Disturbance Decoupling of Max-plus Linear Systems with Applications to a High Throughput Screening System in Drug Discovery

Max-plus linear systems are often used to model timed discrete-event systems, which represent system operations as discrete sequences of events in time. This paper presents the observer-based controller to solve the disturbance decoupling problem for max-plus linear systems where only estimations of system states are available for the controller. This observer-based controller leads to a greater control input than the one obtained with the output feedback strategy based on just-in-time criterion. A high throughput screening system in drug discovery illustrates this main result by showing that the scheduling obtained from the observer-based controller solving the disturbance decoupling problem is better than the scheduling obtained from the output feedback controller

Max-plus (A,B)-invariant spaces and control of timed discrete event systems

The concept of (A,B)-invariant subspace (or controlled invariant) of a linear dynamical system is extended to linear systems over the max-plus semiring. Although this extension presents several difficulties, which are similar to those encountered in the same kind of extension to linear dynamical systems over rings, it appears capable of providing solutions to many control problems like in the cases of linear systems over fields or rings. Sufficient conditions are given for computing the maximal (A,B)-invariant subspace contained in a given space and the existence of linear state feedbacks is discussed. An application to the study of transportation networks which evolve according to a timetable is considered.Comment: 24 pages, 1 Postscript figure, proof of Lemma 1 and some references adde