» Download Article

Authors
Le Corronc, Euriell; Cottenceau, Bertrand; Hardouin, Laurent

Digital Object Identifier (DOI)
10.3182/20100830-3-DE-4013.00066

Page Numbers:
400-405

Index Terms
discrete event dynamic systems,(max,+)-algebra,interval of systems,residuation theory,fixed-point equation theory,optimal control

Abstract
This paper deals with the control of uncertain (max,+)-linear systems, more precisely those of which parameters are not exactly known but assumed to belong to an interval. In this context, we aim at synthesizing a controller in order to reduce the uncertainty at the output of the controlled system. This study is possible thanks to the residuation theory and relies on solutions of fixed-point equations.

References

[1] Baccelli, F., Cohen, G., Olsder, G.J., and Quadrat, J.-P.
    (1992). Synchronisation and linearity: an algebra for
    discrete event systems. Wiley and sons.
[2] Boutin, O., Cottenceau, B., L'Anton, A., and Loiseau,
    J.J. (2009). Modelling systems with periodic routing
    functions in dioid (min,+). In 13th IFAC Symposium
    on Information Control Problems in Manufacturing.
    INCOM'09.
[3] Cottenceau, B., Hardouin, L., Boimond, J.-L., and Ferrier,
    J.-L. (2001). Model reference control for timed event
    graphs in dioids. Automatica, 37(9), 1451-1458.
[4] Cottenceau, B., Lhommeau, M., Hardouin, L., and Boimond,
     J.-L. (2000). Data processing tool for calculation
    in dioid. In 5th International Workshop on Discrete
    Event Systems. WODES'00. http://www.istia.
    univ-angers.fr/~hardouin/outils.html.
[5] Di Loreto, M., Gaubert, S., Katz, R.D., and Loiseau, J.J.
    (2009). Duality between invariant spaces for max-plus
    linear discrete event systems. Eprint arXiv, 0901.2915.
[6] Gaubert, S. (1992). Théorie des systèmes linéaires dans
    les dioïdes. Ph.D. thesis, INRIA - Ecole des Mines de
    Paris.
[7] Heidergott, B., Olsder, G.J., and Woude, J. (2006). Max
    plus at work, modeling and analysis of synchronized systems:
    a course on max-plus algebra and its applications.
    Princeton University Press.
[8] Le Corronc, E., Cottenceau, B., and Hardouin, L. (2009).
    Encadrement de systèmes (min,+)-linéaires. In 7ème
    colloque francophone sur la Modélisation des Systèmes
    Réactifs. MSR'09. http://www.istia.univ-angers.
    fr/~euriell.lecorronc/Recherche/softwares.php.
[9] Lhommeau, M., Hardouin, L., Cottenceau, B., and Jaulin,
    L. (2004). Interval analysis and dioid: application
    to robust controller design for timed event graphs.
    Automatica, 40(11), 1923-1930.
[10] Maia, C.A., Hardouin, L., Santos-Mendes, R., and Cottenceau,
     B. (2005). On the Model Reference Control for
     Max-Plus Linear Systems. In 44th IEEE Conference on
     Decision and Control and European Control Conference.
     CDC-ECC'05, 7799-7803.
[11] MaxPlus (1991). Second order theory of min-linear systems
     and its application to discrete event systems. In
     Proceedings of the 30th IEEE Conference on Decision
     and Control. CDC'91.