Constrained regulation of continuous Petri nets

Nonlinear Analysis: Hybrid Systems

Volumn 3, Issue 4, 2009, Pages 738-748

  Kara, Redouane ^a,b   Ahmane, Mourad ^c   Loiseau, Jean Jacques ^a   Djennoune, Said ^b  

^a INSTITUT DE RECHERCHE EN COMMUNICATIONS ET CYBERNÉTIQUE DE NANTES   (France)

^b UNIVERSITÉ MOULOUD MAMMERI   (Algeria)

^c UNIVERSITÉ DE TECHNOLOGIE DE BELFORT MONTBÉLIARD   (France)

Author keywords

Continuous Petri net; Contractivity; Discrete event systems; Linear Matrix Inequalities (LMI); Polyhedral sets; Positive invariance

Indexed keywords

CONTINUOUS PETRI NET; CONTRACTIVITY; DISCRETE EVENT SYSTEMS; LINEAR MATRIX INEQUALITIES (LMI); POLYHEDRAL SETS; POSITIVE INVARIANCE;

CONTROL SYSTEM STABILITY; FEEDBACK; GRAPH THEORY; LINEAR CONTROL SYSTEMS; PETRI NETS; SWITCHING SYSTEMS;

LINEAR MATRIX INEQUALITIES;

EID: 68849097589     PISSN: 1751570X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nahs.2009.06.011     Document Type: Article

References (29)

1. H. Alla, Réseaux de Petri colorés et réseaux de Petri continus: Application à l'étude des systèmes à événements discrets, Thèse d'état, I.N.P. Grenoble, France, 1987
2. David R., and Alla H. Petri Nets and Grafcet: Tools for Modelling Discrete Event Systems (1993), Prentice-Hall, London
3. Silva M., and Recalde L. Petri nets and integrality relaxations: A view of continuous Petri net models. IEEE Transactions on Systems, Man, and Cybernetics-Part C: Applications and Reviews 32 4 (2002) 314-327
4. Amrah A., Zerhouni N., and El Moudni A. On the control of manufacturing lines modeled by controlled continuous Petri Nets. International Journal of System Science 29 2 (1998) 127-137
5. Mahulea C., Ramirez-Trevino A., Recalde L., and Silva M. Steady-state control reference and token conservation laws in continuous Petri net systems. IEEE Transactions on Automation Science and Engineering 5 2 (2008) 307-320
6. A. Amrah, N. Zerhouni, A. El Moudni, M. Ferney, Constrained state feedback control of a class of discrete event systems modeled by continuous Petri nets, in: Proceedings of ICRACV'96, Westin Stamford, Singapore, 1996
7. R. Kara, S. Djennoune, J.J. Loiseau, State feedback control of discrete event systems modeled by continuous Petri nets, in: Proceedings of INCOM'06, Saint Etienne, France, May 2006
8. Lefebvre D. Feedback control designs for manufacturing systems modeled by continuous Petri nets. International Journal of Systems Sciences 30 6 (1999) 591-600
9. C. Mahulea, A. Giua, L. Recalde, C. Seatzu, M. Silva, On sampling continuous timed PNs: Reachability equivalence under infinite servers semantics, in: 2nd IFAC Conf. on Analysis and Design of Hybrid Systems, Alghero, Italy, June 2006, pp 37-43
10. M. Haouani, D. Lefebvre, A. El Moudni, Neural networks implementation for simulation of manufacturing systems with limited buffers capacities, in: Proceedings of AGI'97 Simulation in Industry, Passau, Germany, 1997
11. S. Hennequin, D. Lefebvre, A. El Moudni, Fuzzy control of variable speed continuous Petri nets, in: Proceedings of the 38th conference on decision and control, Phoenix, Arizona USA, December 1999
12. J. Jùlvez, A. Bemporad, L Recalde, M Silva, Event-driven optimal control of continuous Petri nets, in: Proceedings of 43rd IEEE Conference on Decision and Control, Atlantis, Paradise Island, Bahamas, December 2004
13. Mahulea C., Giua A., Recalde L., Seatzu C., and Silva M. Optimal model predictive control of timed continuous Petri Nets. IEEE Transactions on Automatic Control 53 7 (2008) 1731-1735
14. Silva M., and Recalde L. On fluidification of Petri net models: From discrete to hybrid and continuous models. Annual Reviews in Control 28 (2004) 253-266
15. Decarlo R.A., Branicky M.S., Pettersson S., and Lennartson B. Perspectives and results on the stability and stabilizability of hybrid systems. Proceedings of IEEE 88 7 (2000) (invited paper)
16. Blanchini F. Set invariance in control. Automatica 35 11 (1999) 1747-1767
17. Hennet J.-C. Une extention du lemme de Farkas et son application au problème de régulation linéaire sous contraintes. Comptes Rendus de l'Académie des Sciences Paris 308 I (1989) 415-419
18. Murata T. Petri nets: Properties, analysis and applications. Proceedings of the IEEE 77 4 (1989) 541-580
19. A. Giua, C Mahulea, L. Recalde, C. Seatzu, M. Silva, Optimal control of continuous Petri nets via model predictive control, in: Proceedings of the 8th International Workshop on Discrete Event Systems, Ann Arbor, USA, 2006, pp. 235-241
20. Dorea C.E.T., and Hennet J.C. (A, B)-invariant polyhedral sets of linear discrete-time systems. Journal of Optimization Theory and Applications 103 (1999)
21. Ten Dam A.A., and Nieuwenhuis J.W. A linear programming algorithm for invariant polyhedral sets of discrete-time linear systems. System and Control Lett 25 (1995) 337-341
22. Bitsoris G. Positively invariant polyhedral sets for discrete-time linear systems. International Journal of Control 47 (1988) 1713-1726
23. Bitsoris G. On the positive invariance of polyhedral sets for discrete-time linear systems. Systems and Control Letters 11 (1988) 243-248
24. Milani B.E.A. Piecewise-affine Lyapunov functions for discrete-time linear systems with saturating controls. Automatica 38 12 (2002) 2177-2184
25. Haar A. Uber lineare ungleichungen (1918) Reprinted in: A. Haar, Gesammelte arbeiten, Akademi Kiado, 1959
26. M. Grant, S. Boyd, Y. Ye, CVX: Matlab software for disciplined convex programming (web page and software), Available at www.stanford.edu/~boyd/cvx/, May 2008
27. Grant M., and Boyd S. Graph implementations for nonsmooth convex programs. In: Blondel V., Boyd S., and Kimura H. (Eds). Recent Advances in Learning and Control (a tribute to M. Vidyasagar). Lecture Notes in Control and Information Sciences (2008), Springer 95-110. http://stanford.edu/~boyd/graph_dcp.html
28. Gahinet P., Nemirovskii A., Laub A.J., and Chilali M. LMI Control Toolbox Users Guide (1995), The MathWorks Inc., Natick, MA
29. R. David, H. Alla, Continuous Petri nets, in: Proceedings of the 8th European Workshop on Application and Theory of Petri Nets, Zaragoza, Spain, 1987, pp. 275-294