146
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Supervisory control of (max,+) automata: extensions towards applications

, &
Pages 2523-2537 | Received 18 Nov 2014, Accepted 01 May 2015, Published online: 09 Jun 2015

References

  • Amari, S., Demongodin, I., Loiseau, J.J., & Martinez, C. (2012). Max-plus control design for temporal constraints meeting in timed event graphs. IEEE TAC, 57, 462–467.
  • Baccelli, F., Cohen, G., Olsder, G.J., & Quadrat, J.P. (1992). Synchronization and linearity. New York, NY: Wiley.
  • Badouel, E., Bouillard, A., Darondeau, P., & Komenda, J. (2011). Residuation of tropical series: Rationality issues (Rapport de recherche 7547). Rennes, France: INRIA.
  • Benveniste, A., Gaubert, S., & Jard, C. (1998). Monotone rational series and max-plus algebraic models of real-time systems. In Proceedings of the Fourth Workshop on Discrete Event Systems. Cagliari, Italy.
  • Berstel, J., & Reutenauer, C. (1988). Rational series and their languages. Berlin: Springer Verlag.
  • Blyth, T.S., & Janowitz, M.F. (1972). Residuation theory. Oxford/New York: Pergamon Press.
  • Boimond, J.L., & Ferrier, J.L. (1996). Internal model control and max-algebra: Controller design. IEEE Transactions on Automatic Control, 41, 457–461.
  • Brandin, B.A., & Wonham, W.M. (1994). Supervisory control of timed discrete-event systems. IEEE Transactions on Automatic Control, 39, 329–342.
  • Buy, U., Darabi, H., Lehene, M., & Venepally, V. (2005). Supervisory control of time Petri nets using net unfolding. In Proceedings of the 29th Annual International Conference on Computer Software and Applications Conference (pp. 97–100). COMPSAC-W’05. Washington, DC: IEEE Computer Society.
  • Cassandras, C.G., & Lafortune, S. (2006). Introduction to DES. New York: Springer-Verlag.
  • Cohen, G., Moller, P., Quadrat, J.P., & Viot, M. (1989). Algebraic tools for the performance evaluation of discrete event systems. IEEE Proceedings: Special issue on Discrete Event Systems, 77 (1), 39–58.
  • David, R., & Alla, H. (2010). Discrete, continuous, and hybrid Petri Nets (2nd ed.). Paris: Springer.
  • De Schutter, B., & van den Boom, T. (2001). Model predictive control for max-plus-linear discrete event systems. Automatica, 37, 1049–1056.
  • Gaubert, S. (1995). Performance evaluation of (max,+) automata. IEEE TAC, 40, 2014–2025.
  • Gaubert, S., & Mairesse, J. (1999a). Asymptotic analysis of heaps of pieces and application to timed Petri nets. In Proceedings of the 8th International Workshop on Petri Nets and Performance Models (pp. 158–169). Zaragoza: IEEE Computer Society.
  • Gaubert, S., & Mairesse, J. (1999b). Modeling and analysis of timed Petri nets using heaps of pieces.. IEEE TAC, 44, 683–698.
  • Heidergott, B., Olsder, G.J., & Woude, J.V.D. (2006). Max plus at work. Princeton, NJ: Princeton Press.
  • Heidira, P., & Boucheneb, H. (2013). Maximally permissive controller synthesis for time Petri nets. International Journal of Control, 86, 1–6.
  • Houssin, L. (2011). Cyclic jobshop problem and (max,plus) algebra. In S. Bittanti, A. Cenedese, & S. Zampieri (Eds.), 18th IFAC WC. (pp. 2717–2721). Milan: IFAC.
  • Houssin, L., Lahaye, S., & Boimond, J.L. (2013). Control of constrained (max,+)-linear systems minimizing delays. Discrete Event Dynamic Systems., 23, 261–273
  • Kirsten, D. (2008). A burnside approach to the termination of Mohri's algorithm for polynomially ambiguous min-plus-automata. RAIRO – Theoretical Informatics and Applications, 42, 553–581.
  • Klimann, I., Lombardy, S., Mairesse, J., & Prieur, C. (2004). Deciding unambiguity and sequentiality from a finitely ambiguous max-plus automaton. Theoretical Computer Science, 327 (3), 349–373.
  • Komenda, J., Lahaye, S., & Boimond, J.L. (2009). Supervisory control of (max,+) automata: A behavioral approach. Discrete Event Dynamic Systems, 19, 525–549.
  • Komenda, J., Lahaye, S., & Boimond, J.L. (2013). Séquentialisation des réseaux de Petri temporisés. [Sequentialization of timed Petri nets] Journal Européen des Systèmes Automatisés (Special issue including the proceedings of MSR 2013), 43, 139–154.
  • Lafortune, S., & Chen, E. (1990). The infimal closed and controllable superlanguage and its applications in supervisory control. IEEE Transactions on Automatic Control, 35, 398–405.
  • Lahaye, S., Boimond, J.L., & Ferrier, J.L. (2008). Just in time control of time-varying discrete event dynamic systems in (max,+) algebra. International Journal of Production Research (IJPR), 46, 5337–5348.
  • Lahaye, S., Komenda, J., & Boimond, J.L. (2014a). Compositions of (max,+) automata. Discrete Event Dynamic Systems. DOI 10.1007/s10626-014-0186-6.
  • Lahaye, S., Komenda, J., & Boimond, J.L. (2014b, May). Modeling of timed Petri nets using deterministic (max, +) automata. In J.-J. Lesage, J.E.R. Cury, & B. Lennartson, (Eds.) Proceedings of WODES. (pp. 471–476) Cachan: IEEE-IFAC.
  • Lhommeau, M., Hardouin, L., Cottenceau, B., & Jaulin, L. (2004). Interval analysis in diod: Application to robust controller design for timed event graphs. Automatica, 40, 1923–1930.
  • Lin, F., & Wonham, W.M. (1988). On observability of discrete-event systems. Information Sciences, 44, 173–198.
  • Lombardy, S., & Mairesse, J. (2006). Series which are both max-plus and min-plus rational are unambiguous. RAIRO - Theoretical Informatics and Applications, 40, 1–14.
  • Lombardy, S., & Sakarovitch, J. (2006). Sequential ? Theoretical Computer Science, 359, 224–244.
  • Murata, T. (1989). Petri nets: Properties, analysis and applications. IEEE Proceedings: Special issue on Discrete Event Systems, 77, 541–580.
  • Ramadge, P.J.G., & Wonham, W.M. (1989). The control of discrete event systems. Proceedings of The IEEE, 77, 81–98.
  • Su, R., van Schuppen, J., & Rooda, J. (2012). The synthesis of time optimal supervisors by using heaps-of-pieces. IEEE TAC, 57, 105–118.
  • Wong-Toi, H., & Hoffmann, G. (1995). The control of dense real-time discrete event systems. (Technical Report STA-CS-92-1411). Stanford: Stanford University.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.