Abstract
The aim of this paper is the predictive control of Timed Event Graphs with specifications defined by P-time Event Graphs. We propose a fixed-point approach which leads to a pseudo-polynomial algorithm. As the performance of the algorithm is crucial in on-line control, we highlight an important case where the resolution of this first algorithm is efficient. The second technique is a space controller on a horizon leading to a strongly polynomial algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Amari S, Demongodin I, Loiseau JJ (2004) Sizing and cycle time of an industrial plant using dioid algebra. In: Dolgui A, Soldek J, Zaikin O (eds) Supply chain optimization. Series applied optimization, chapter 6. Springer, New York, pp 71–85
Baccelli F, Cohen G, Olsder GJ, Quadrat JP (1992) Synchronization and linearity. An algebra for discrete event systems. Wiley, New York. Available from http://maxplus.org
Birkhoff G (1967) Lattice theory. American Mathematical Society, Providence
Declerck P (2011) From extremal trajectories to consistency in P-time Event Graphs. IEEE Trans Aut Control (IETAA9) 56(2):463–467. Available from http://www.istia.univ-angers.fr/~declerck
Declerck P, Didi Alaoui MK (2010) Optimal control synthesis of Timed Event Graphs with interval model specifications. IEEE Trans Aut Control (IETAA9) 55(2):518–523. Available from http://www.istia.univ-angers.fr/~declerck
De Schutter B, van den Boom T (2001) Model predictive control for max-plus-linear discrete event systems. Automatica 37(7):1049–1056
Gaubert S (1998) Two lectures on max-plus algebra. In: Proceedings of the 26th spring school on theoretical computer science and automatic control, Noirmoutier
Hashtrudi Zad S, Kwong RH, Wonham WM (1999) Supremum operators and computation of supremal elements in system theory. SIAM J Control Optim 37(3):695–709
Katz RD (2007) Max-plus (A,B)—invariant spaces and control of Timed Discrete-Event Systems. IEEE Trans Aut Control 52(2):229–241
Khansa W (1997) Réseaux de Petri P-temporels. Contribution à l’étude des Systèmes à Evénements Discrets. Ph.D. thesis, University of Savoie
Libeaut L, Loiseau JJ (1995) Admissible initial conditions and control of Timed Event Graphs. In: 34th conference on decision and control, CDC’95, New Orleans, Louisianna
McMillan K, Dill D (1992) Algorithms for interface timing verification. In: Proceedings of the IEEE, international conference on computer design: VLSI in computers and processors
Schrijver A (1986) Theory of linear and integer programming. In: Wiley-Interscience series in discrete mathematics and optimization. Wiley, New York
Tarski A (1955) A lattice-theoretical fixpoint theorem and its applications. Pac J Math 5:285–309
Walkup E (1995) Optimization of linear max-plus systems with application to timing analysis. Ph.D. thesis, University of Washington
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Declerck, P., Guezzi, A. Predictive control of Timed Event Graphs with specifications defined by P-time Event Graphs. Discrete Event Dyn Syst 24, 261–273 (2014). https://doi.org/10.1007/s10626-012-0150-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10626-012-0150-2