Commande prédictive des systèmes dynamiques hybrides

Commande prédictive des systèmes dynamiques hybrides

Marwa Taleb Edouard Leclercq Dimitri Lefebvre 

Groupe de Recherche en Électrotechnique et Automatique du Havre 75 rue bellot Cs 80540, BP 76600 Le Havre, France

Corresponding Author Email: 
{marwa.taleb,edouard.leclercq,dimitri.lefebvre}@univ-lehavre.fr
Page: 
49-74
|
DOI: 
https://doi.org/10.3166/JESA.50.49-74
| |
Published: 
30 April 2017
| Citation
Abstract: 

RÉSUMÉ. Cet article concerne le problème de commande prédictive des systèmes dynamiques hybrides (SDH) modélisés par réseaux de Petri hybrides (RdPH) élémentaires avec des transitions immédiates et/ou temporisées. Le but est de piloter ces systèmes afin d’atteindre un marquage désiré. Étant donné que le SDH intègre à la fois des processus continus et discrets en interaction, la commande hybride proposée est composée d’actions de commande continues et discrètes. A chaque pas d’échantillonnage, la commande prédictive discrète explore partiellement le graphe d’atteignabilité et détermine l’ensemble des séquences de commandes réalisables de taille bornée. La commande prédictive continue calcule, pour chacune de ces séquences, la commande constante associée sur un horizon de prédiction continu variable, afin de choisir la commande hybride optimale qui minimise un critère de performance.

ABSTRACT. This paper addresses the predictive control design of Hybrid Dynamic Systems (HDS) modeled by Elementary Hybrid Petri Net (HPN) systems with timed and/or immediate discrete transitions. Our goal is to drive a HPN to reach a desired marking. Since HDS incorporates both discrete and continuous processes, the proposed control strategy, called Hybrid Predictive Control, is composed of discrete and continuous predictive control actions. At each sampling period, the discrete control explores a portion of the reachability graph and selects a set of feasible control sequences whose length is upper bounded. The continuous predictive control computes, for each sequence, the corresponding continuous constant control action, over a variable continuous prediction horizon, in order to find the optimal hybrid control that minimizes a certain cost function.

Keywords: 

réseau de Petri continu, réseau de Petri discret, réseau de Petri hybride élémentaire, commande prédictive

1. Introduction
2. Réseaux de Petri hybrides
3. Commande prédictive hybride
4. Commande prédictive hybride avec des transitions discrètes non immédiates
5. Conclusion
  References

Alla H., Ghomri L. (2012). Modeling and simulation by hybrid Petri nets. In Proceedings of the 2012 winter simulation conference, p. 1-8. Berlin.

Balduzzi F., Giua A., Menga G. (2000). First-order hybrid Petri nets: a model for optimization and control. IEEE Transactions on Robotics and Automation, vol. 16, no 4, p. 382-399.

Bemporad A., Morari M., Dua V., Pistikopoulos E. N. (2002). The explicit linear quadratic regulator for constrained systems. Automatica, vol. 38, no 1, p. 3-20.

David R., Alla H. (1992). Petri nets and grafcet: tools for modeling discrete event systems (P. Hall, Ed.). London.

David R., Alla H. (2001). On hybrid Petri nets. Discrete Event Dynamic Systems: Theory and Applications, vol. 11, p. 9-40.

Dotoli M., Fanti M. P., Iacobellis G., Mangini A. M. (2009). A first-order hybrid Petri net model for supply chain management. IEEE Transactions on Automation Science and Engineering, vol. 6, no 4, p. 744-758.

Fanti M. P., Iacobellis G., Maangini A. M., Ukovich W. (2014). Freeway traffic modeling and control in a first-order hybrid Petri net framework. IEEE Transactions on Automation Science and Engineering, vol. 11, no 1, p. 90-102.

Geletu A. (2007, December 13). Solving optimization problems using the matlab optimization toolbox - a tutorial.

Ghomri L., Alla H. (2007). Modeling and analysis using hybrid Petri nets. Nonlinear Analysis: Hybrid Systems, vol. 1, no 2, p. 141-153.

Giua A., Mahulea C., Recalde L., Seatzu C., Silva M. (2006). Optimal control of continuous Petri nets via model predictive control. In 8th international workshop on discrete event systems, p. 235-241. Ann Arbor, Michigan, USA.

Gudino-Mendoza B., Lopez-Mellado E. (2013). Modelling networked agents’ behaviour using timed hybrid Petri nets. In 3rd iberoamerican conference on electronics engineering and computer science, vol. 7, p. 289-296. San Luis Potosi, Mexico.

Julvez J., Bemporad A., Recalde L., Silva M. (2004). Event-driven optimal control of continuous Petri nets. In 43rd IEEE conference on decision and control, p. 69-74. Atlantis, Paradise Island, Bahamas.

Julvez J., Cairano S. D., Bemporad A., Mahulea C. (2013). Event-driven model preditcive control of timed Petri nets. International Journal of Robust and Nonlinear Control, vol. 24, no 12, p. 1724-1742.

Julvez J., Mahulea C., Vasquez C. (2011). Analysis and simulation of manufacturing systems using simhpn toolbox. In 2011 IEEE conference on automation science and engineering, p. 432-437. Trieste, Italy.

Kaakai F., Hayat S., Moudni A. E. (2006). Simulation of railway stations based on hybrid Petri nets. In 2nd ifac conference on analysis and design of hybrid systems, vol. 39, p. 50-55. Alghero, Italy.

Lefebvre D., Leclercq E. (2015). Control design for trajectory tracking with untimed Petri nets. IEEE Transactions on Automatic Control, vol. 60, no 7, p. 1921-1926.

Lefebvre D., Leclercq E., Druaux F., Thomas P. (2015). Gradient-based controllers for timed continuous Petri nets. International Journal of Systems Science, Taylor & Francis, vol. 46, no 9, p. 1661-1678.

Mahulea C., Giua A., Recalde L., Seatzu C., Silva M. (2008). Optimal model predictive control of timed continuous Petri nets. IEEE Transactions on Automatic and Control, vol. 53, no 7, p. 1731-1735.

Mahulea C., Ramirez-Trevino A., Recalde L., Silva M. (2008). Steady state control reference and token conservation laws in continuous Petri net systems. IEEE Transactions on Automation Science and Engineering, vol. 5, no 2, p. 307-320.

Mahulea C., Recalde L., Seatzu C., Silva M. (2006). On sampling continuous timed pns: Reachability "equivalence" under infinite servers semantics. In 2nd ifac conference on analysis and design of hybrid systems, vol. 39, p. 37-43. Alghero, Italy.

Richalet J., Rault A., Testud J., Papon J. (1978). Model predictive heuristic control: Applications to industrial processes. Automatica, vol. 14, no 5, p. 413-428.

Silva M. (1993). Introducing Petri nets. Practice of Petri Nets in manufacturing.

Silva M., Recalde L. (2002). Petri nets and integrity relaxations: A view of continuous Petri net models. IEEE-Transactions Systems Man and Cybernetics, part C, vol. 32, no 4, p. 314-327.

Silva M., Recalde L. (2004). On fluidification of Petri net models: from discrete to hybrid and continuous models. Annual Reviews in Control, vol. 28, no 2, p. 253-206.

Taleb M., Leclercq E., Lefebvre D. (2014a). Limitation of flow variation of continuous Petri nets via model predictive control. In Americain control conference, p. 4919-4924. Portland, Oregon.

Taleb M., Leclercq E., Lefebvre D. (2014b). Limitation of flow variation of continuous Petri nets via model predictive control and lyapunov criterion. In European control conference, p. 1825-1830. Strasbourg, France.

Taleb M., Leclercq E., Lefebvre D. (2016). Model predictive control for discrete and continuous timed Petri nets. International Journal of Automation and Computing. (accepté pour publication)

Tolba C., Lefebvre D., Thomas P., Moudni A. E. (2005). Continuous and timed Petri nets for the macroscopic and microscopic traffic flow modeling. Simulation Modeling Practice and Theory, vol. 13, no 5, p. 407-436.