Laurent Hardouin

Brief Model reference control for timed event graphs in dioids

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.

Optimal closed-loop control of timed EventGraphs in dioids

This note deals with the model-reference control of timed event graphs using the dioid algebra and the residuation theory. It proposes a control structure based on a precompensator and a feedback controller to improve the controlled system performance. It is shown that this approach always leads to an optimal behavior of the closed-loop system. An example is given to illustrate the proposed approach.

Just-in-time control of timed event graphs: update of reference input, presence of uncontrollable input

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.

Interval analysis and dioid: application to robust controller design for timed event graphs

This paper deals with feedback controller synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a robust controller set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each controller is computed in order to guarantee that the closed-loop system behavior is greater than the lower bound of a reference model set and is lower than the upper bound of this set. The synthesis presented here is mainly based on dioid, interval analysis and residuation theory.

A First Step Towards Adaptive Control for Linear Systemsin Max Algebra

Alinear system theory has been developed for discrete event systemssubject to synchronization. We are interested in the just intime control of such systems in presence of a possible mismatchbetween the system and its model. Taking such mismatch into accountin controller synthesis prevents us from using the usual openloop control structure. The approach we propose to synthesizethe controller is inspired by the principle of the indirect adaptivecontrol well known in conventional system theory. Its designleads to solve an optimal tracking problem under an equalityconstraint. Preliminary results about the estimation of modelsare presented.

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 systems performance.

Brief paper: On the control of max-plus linear system subject to state restriction

This paper deals with the control of discrete event systems subject to synchronization and time delay phenomena, which can be described by using the max-plus algebra. The objective is to design a feedback controller to guarantee that the system evolves without violating time restrictions imposed on the state. To this end an equation is derived, which involves the system, the feedback and the restriction matrices. Conditions concerning the existence of a feedback are discussed and sufficient conditions that ensure the computation of a causal feedback are presented. To illustrate the results of this paper, a workshop control problem is presented.

On the Model Reference Control for Max-Plus Linear Systems

This paper deals with the model-reference control of max-plus linear systems. The main contribution of this work is a general control structure that encompasses the previous one found in the literature. It is based on the RST-structure for conventional differentiable system. In addition it provides a comparison among some sub-structures and simulation results are presented.

Observer Design for

This technical note deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state. The observer design is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring.

(\max, +)

Abstract This paper presents a design method for a state observer of max-plus linear systems based on the observation of the input and the output, by assuming the knowledge of the system matrices. The observer design is done in an analogous way to the observer method for classical linear system. The paper will be concluded by an illustration.