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    Max-Plus filtering

    Max-Plus filtering

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    Research project

    «Filtering of max-plus dynamic systems»



    Team: Dynamic and discrete events and Optimization


    Labeling: none

    Term: from 01/09/2016 until 01/03/2018


    Funding: Atlanstic RFI 2020


    LARIS staff involved: Mehdi Lhommeau, Laurent Hardouin


    Project partners: Department of Computer Engineering and Industrial Automation DCA, School of Elecctrical and Computer Engineering, State University of Campinas - UNICAMP, Campinas, SP, Brazil (Pr. Rafael Santos Mendes)



    The theory of dynamic systems with discrete events has been formed in recent years from the study of production systems, transport networks, computer systems, ... It is interested in performance evaluation problems (computation production rate, flow rate), verification and control synthesis questions (need to satisfy certain logical constraints, such as the absence of blocking or mutual exclusion, the continuation of a set path, etc...), as well as optimization problems (eg optimal number of processors or machines to perform a given task).

    The common point of the studied systems is the presence of phenomena of synchronization, saturation or competition related to the occurrence of events (arrival of a client, interruption of a task, ...) which seem to prohibit the use of the tools familiar to the automation engineer (differential equations, recurrent equations, ...).

    For several years, the LARIS SDO team has been interested in the study of these systems in the theoretical framework of max-plus algebra. Many fundamental problems have been studied, for example the problem of control with reference model, the robust controller synthesis, the rejection of disturbance, ... 

    In most of the applications considered in these works, the state of the system can not be completely known, because some state variables are not accessible to measurement, and inevitable measurement errors, or measurement noise, or uncertainty on the system intervene.

    Our goal is to develop a filtering theory for dynamic discrete event systems described in max-plus algebra. Indeed, being able to reconstruct the state of the system from the result of measurements, usually noisy, is a major issue. It is in this sense, that we began work, from 2012, through the co-supervision of a research master, between the LARIS SDO team and the team of Professor Rafael Santos Mendes of the Department of Computer Engineering and Industrial Automation (DCA-FEEC - UNICAMP) in Brazil. The work of this Brazilian student, Renato Markele, gave rise to a paper at the ECC2013 conference. The student Renato Markele Ferreira Cândido continues this work through a co-supervision thesis, started in January 2015, between LARIS and DCA-FEEC - UNICAMP.


    We wish to continue this research by following three axes:

    • extend recent work on the use of bounded difference matrices for the max-plus dynamic system achievable set computation to the filtering problem;
    • lift the hypotheses on the choice of the support of the density of probability;
    • extend filtering to unreliable max-plus dynamic systems;


    The first six months will be devoted to theoretical work on the application of matrices of differences limited to the problem of filtering. This should enable us to make assumptions about the choice of support for the probability density. Finally, the last six months will allow the writing of major articles and the continuation of theoretical work on the extension of filtering to uncertain dynamic systems.


    The collaboration between LARIS and DCA-FEEC will be facilitated by the presence at LARIS, of Prof. Rafael Santos Mendes. Indeed, he obtained a chair of excellence to stay one year (2016-2017) within LARIS in Angers.



    Contact: mehdi.lhommeau @ univ-angers.fr