Control Strategies For Referential Modeling Of Systems Involving Discrete Events By Linear Max-plus [estratégias De Controle Por Modelo De Referência De Sistemas A Eventos Discretos Max-plus Lineares]

This paper deals with the control of discrete event systems modelled by the Max-plus algebra. This approach is used to describe processes whose dynamics are characterized by time delay and synchronization phenomena. Typical examples of these processes are assembly lines in manufacturing systems. The studied control problem is related to the just-in-time strategy for production planning. In this tutorial paper, several strategies based on the model reference control approach are presented, exemplified and discussed.163263278Antsaklis, A.J., A brief introduction to the theory and applications of hybrid systems (2000) Proceedings of the IEEE, 88 (7), pp. 879-887. , Special Issue on Hybrid Systems: Theory and ApplicationsBaccelli, F., Cohen, G., Olsder, G., Quadrat, J., (1992) Synchronisation and Linearity: An Algebra for Discrete Event Systems, , John Wiley and Sons, New YorkBanks, J., Carson, J.S., Nelson, B.L., Nicol, D.M., (2000) Discrete-event System Simulation, 3rd. Edn, , Prentice-HallBlyth, T., Janowitz, M., (1972) Residuation Theory, , Pergamon Press, OxfordBoimond, J., Ferrier, J., Internal model control and max-algebra: Controller design (1996) IEEE TAC, 41 (3), pp. 457-461Cassandras, C.G., Lafortune, S., (1999) Introduction to Discrete Event Systems, , Kluwer Academic PublishersCohen, G., Gaubert, S., Quadrat, J.-P., Max-plus algebra and system theory: Where we are and where to go now (1999) Annual Reviews in Control, 23, pp. 207-219Cohen, G., Moller, P., Quadrat, J., Viot, M., Algebraic tools for the performance evaluation of discrete event systems (1989) IEEE Proceedings: Special Issue on Discrete Event Systems, 77 (1), pp. 39-58Commault, C., Feedback stabilization of some event graph models (1998) IEEE Trans. on Automatic Control, 43 (10), pp. 1419-1423Cottenceau, B., (1999) Contribution à la Commande de Systèmes à Événements Discrets: Synthèse de Correcteurs pour les Graphes d'Ev́eńements Temporisés dans les Dioïdes, , Thèse de doctorat, Université d'Angers, Angers - FranceCottenceau, B., Hardouin, L., Boimond, J., Ferrier, J., Synthesis of greatest linear feedback for timed event graphs in dioid (1999) IEEE Trans. on Automatic Control, 44 (6), pp. 1258-1262Cottenceau, B., Hardouin, L., Boimond, J., Ferrier, J., Model reference control for timed event graphs in dioid (2001) Automatica, 37, pp. 1451-1458Cuninghame-Green, R., Minimax algebra (1979) Lecture Notes in Economics and Mathematical Systems, , number 166, Springer-Verlag, BerlinHardouin, L., (2004) Sur la Commande Linéaire de Systèmes à Evenements Discrets dans l'Algeb̀re (Max,+), , Habilitation à diriger des recherches, Université d'Angers, Angers - FranceKleinrock, L., (1975) Queueing Systems - Theory, 1. , Wiley-InterscienceLahaye, S., Boimond, J., Hardouin, L., Linear periodic systems over dioids (2004) Discrete Event Dynamic Systems - Theory and Applications, 14 (2), pp. 133-152Lhommeau, M., Hardouin, L., (2003) Software Tools for Manipulating Periodic Series, , http://www.istia-angers.fr/~hardouin/outils.htmlLhommeau, M., Hardouin, L., Cottenceau, B., Jaulin, L., Interval analysis and dioid: Application to robust controller design for timed event graphs (2004) Automatica, 40, pp. 1923-1930Lüders, R., (2001) Controle Multivariável de Sistemas a Eventas Discretos em Dióides, , Tese de doutorado, UNICAMP, Campinas,SP, BrasilLüders, R., Santos-Mendes, R., Generalized multivariable control of discrete event systems in dioid (2002) 6th International Workshop on Discrete Event Systems (WODES'02), , Zaragoza, SpainMaia, C.A., (2003) Identificação e Controle de Sistemas a Eventas Discretos na Álgebra (Max,+), , Tese de doutorado, UNICAMP, Campinas, SP, BrasilMaia, C.A., Hardouin, L., Santos-Mendes, R., Cottenceau, B., Optimal closed-loop control of timed event graphs in dioids (2003) IEEE Trans. on Automatic Control, 48 (12), pp. 2284-2287Menguy, E., Boimond, J., Hardouin, L., Ferrier, J., A first step towards adaptive control for linear systems in max algebra (2000) Discrete Event Dynamic Systems. Theory and Applications, 10, pp. 347-367Murata, T., Petri nets: Properties, analysis and applications (1989) Proceedings of the IEEE, 77 (4), pp. 541-580Ostroff, J., (1989) Temporal Logic for Real-time Systems, , John Wiley, New YorkRamadge, P., Wonham, W., The control of discrete event systems (1989) IEEE TAC, 77, pp. 81-98Wang, J., (1998) Timed Petri Nets, , Kluwer Academic Publisher