Información del artículo
Resumen
Gracias a la existencia de potentes teorías de análisis y síntesis, asf corno a su directa representabilidad gràfica, las redes de Petri constituyen uno de los formalismos más aceptados en las aplicaciones de ingeniería en las que convienen modelos (de eventos) discretos. No obstante, a veces surgen problemas de decidibilidad o, en sistemas con grandes poblaciones, de enorme complejidad computacional. En este trabajo se presenta la urdimbre y algunos flecos de la teoría desarrollada para una relajación fluida o continua de los modelos discretos y dinámicos. Con ella se puede abordar eficientemente el estudio de sistemas de otra forma no abordables, al tiempo que se establecen algunos puentes a conceptos y resultados del análisis y síntesis de prestaciones, o de la observación y control de sistemas denominados continuos, aunque las clases de modelos que se obtienen son técnicamente, a veces también conceptualmente, híbridos. Obviamente, el precio que se paga por toda relajación es una pérdida de fidelidad en los modelos. En este sentido se ha de tener en cuenta que, aunque insólito en aplicaciones de ingeniería, los modelos discretos pueden ser no continuizables, del mismo modo que no todo sistema continuo no-lineal se puede aproximar satisfactoriamente por uno lineal (piénsese, por ejemplo, en sistemas caóticos).
Palabras clave:
Red de Petri
ciclo de vida
relajación matemática
teoría estructural
análisis cualitativo
análisis cuantitativo
optimización paramétrica
observación y control dinámico
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Referencias
[Ajmone Marsan et al., 1995]
M. Ajmone Marsan, G. Balbo, G. Conte, S. Donatelli, G. Franceschinis.
Modelling with Generalized Stochastic Petri Nets.
Wiley, (1995),
[Alla and David, 1998]
H. Alla, R. David.
Continuous y hybrid Petri nets.
Journal of Circuits, Systems, and Computers, 8 (1998), pp. 159-188
[Bemporad et al., 2000]
Bemporad, A., F.D. Torrisi y M. Morari (2000). Performance analysis of piecewise linear systems and model predictive control systems. Proc. of the 39th IEEE Conference on Decision and Control. Sydney, Australia, pp. 4957–4962.
[Brams, 1983]
G.W. Brams.
Réseaux de Petri: Théorie et Pratique.
Masson, (1983),
[Champagnat et al., 1998]
R. Champagnat, P. Esteban, H. Pingaud, R. Va-lette.
Modeling and simulation of a hybrid system through Pr/Tr PN-DAE model.
Proc. of ADPM’98, pp. 131-137
[Champagnat et al., 2001]
R. Champagnat, R. Valette, J.C. Hochon, H. Pingaud.
Modeling, simulation and analysis of batch production systems.
Discrete Event Dynamic Systems: Theory and Application, 11 (2001), pp. 119-136
[Chen et al., 2003]
B.M. Chen, T.H. Lee, K. Peng, V. Venkatara-manan.
Composite nonlinear feedback control for linear systems with input saturation: theory and an application.
IEEE Trans, on Automatic Control, 48 (2003), pp. 427-439
[Chen and Yao, 2001]
Chen, H. y D.D. Yao (2001). Fundamentals of Queueing Networks. Performance, Asympto-tics and Optimization. Vol. 46 of Applications of Mathematics. Stochastic Modelling and Applied Probability. Springer.
[David and Alla, 1992]
R. David, H. Alla.
Petri Nets and Grafcet.
Prentice-Hall, (1992),
[David and Alla, 2004]
R. David, H. Alla.
Discrete, Continuous, and Hybrid Petri Nets.
Springer-Verlag, (2004),
[Demongodin and Koussoulas, 1998]
I. Demongodin, N.T. Koussoulas.
Differential Petri nets: Representing continuous systems in a discrete-event world.
IEEE Trans. on Automatic Control (Special Issue), 43 (1998), pp. 573-579
[Dicesare et al., 1993]
F. Dicesare, G. Harhalakis, J.M. Proth, M. Silva, F.B. Vernadat.
Practice of Petri Nets in Manufacturing.
Chapman & Hall, (1993),
[Haddad et al., 2006]
S. Haddad, L. Recalde, M. Silva.
On the computational power of Timed Differentiable Petri nets.
Formal Modeling and Analysis of Timed Systems, 4th Int. Conf. FORMATS 2006, pp. 230-244
[Horton et al., 1998]
G. Horton, V.G. Kulkarni, D.M. Nicol, K.S. Trivedi.
Fluid stochastic Petri nets: Theory, applications, and solution techniques.
European Journal of Operational Research, 105 (1998), pp. 184-201
[Jensen, 1997]
K. Jensen.
Coloured Petri Nets: Basic Concepts, Analysis Methods, and Practical Use, Springer, (1997),
[Jiménez et al., 2004]
Jiménez, E., J. Júlvez, L. Recalde y M. Silva (2004). Relaxed continuous views of discrete event systems: considerations in Forrester diagrams and Petri nets. In: Proc. of the Int. Conf. on Systems, Man and Cybernetics (SMC 2004). The Hague, The Netherlands. pp. 4897–4904.
[Júlvez et al., 2004]
J. Júlvez, E. Jimenez, L. Recalde, M. Silva.
On observability in timed continuous Petri net systems.
Proc. of the 1st Int. Conf. on the Quantitative Evaluation of Systems (QEST 2004), pp. 60-69
[Júlvez et al., 2003]
J. Júlvez, L. Recalde, M. Silva.
On reachability in autonomous continuous Petri net systems.
Proc. of the 24th Int. Conf. on Application and Theory of Petri Nets (ICATPN 2003), pp. 221-240
[Júlvez et al., 2005]
J. Júlvez, L. Recalde, M. Silva.
Steady-state performance evaluation of continuous mono-t-semiflow Petri nets.
Automatica, 41 (2005), pp. 605-616
[Júlvez et al., 2006]
J. Júlvez, L. Recalde, M. Silva.
Deadlock-freeness analysis of continuous mono-t-semiflow petri nets.
IEEE Trans. on Automatic Control, 51 (2006), pp. 1472-1481
[Lien, 1998]
Y.E. Lien.
Toward improvement of tracking performance - nonlinear feedback for linear systems.
International Journal of Control, 70 (1998), pp. 1-11
[Mahulea et al., 2006a]
Mahulea, C., A. Giua, L. Recalde, C. Seatzu y M. Silva (2006a). On sampling continuous timed Petri nets: reachability “equivalence” under infinite servers semantics. In: 2nd IFAC Conference on Analysis and Design of Hybrid Systems, ADHS06. Alghero, Italy. pp. 37–43.
[Mahulea et al., 2007]
C. Mahulea, A. Ramirez-Trevino, L. Recalde, M. Silva.
Steady state control reference and token conservation laws in continuous Petri net systems.
IEEE Trans. on Automation Science and Engineering, (2007),
[Mahulea et al., 2006b]
C. Mahulea, L. Recalde, M. Silva.
On performance monotonicity and basic servers semantics of continuous Petri nets.
8th Int. Workshop on Discrete Event Systems WODES06, pp. 345-351
[Mandelbau and Chen, 1991]
A. Mandelbau, H. Chen.
Discrete flow networks: Bottleneck analysis and fluid approximations.
Mathematical Operations Research, 16 (1991), pp. 408-446
[Molloy, 1982]
M.K. Molloy.
Performance analysis using stochastic Petri nets.
IEEE Trans. on Computers, 31 (1982), pp. 913-917
[Mosekilde et al., 1988]
E. Mosekilde, J. Aracil, P.M. Allen.
Instabilities and chaos in nonlinear dynamic systems.
Systems Dynamics Review, 4 (1988), pp. 14-55
[Murty, 1983]
K.G. Murty.
Linear Programming.
Wiley and Sons, (1983),
[Nicolis and Prigogine, 1971]
G. Nicolis, I. Prigogine.
Fluctuations in nonequilibrium systems.
Proc. Nat. Acad. Sci. U.S.A., 68 (1971), pp. 2102-2107
[Peterson, 1981]
J.L. Peterson.
Petri Net Theory and the Modeling of Systems.
Prentice-Hall, (1981),
[Recalde and Silva, 2001]
L. Recalde, M. Silva.
Petri Nets fluidification revisited: Semantics and steady state.
European Journal of Automation APII-JESA, 35 (2001), pp. 435-449
[Recalde et al., 1999]
L. Recalde, E. Teruel, M. Silva.
Autonomous continuous P/T systems.
Application and Theory of Petri Nets 1999, pp. 107-126
[Recalde et al., 2007]
Recalde, L., S. Haddad y M. Silva (2007). Continuous Petri nets: Expressive power and decidability issues. Research report. Dep. Informática e Ingenierá de Sistemas, Universidad de Zaragoza. Mará de Luna, 1, 50018 Zaragoza, Spain.
[Saberi et al., 1996]
A. Saberi, Z. Lin, A.R. Teel.
Control of linear system with saturating actuators.
IEEE Trans. on Automatic Control, 41 (1996), pp. 368-378
[Silva, 1993]
M. Silva.
Introducing Petri nets.
Practice of Petri Nets in Manufacturing, (1993), pp. 1-62
[Silva, 2002]
M. Silva.
Las Redes de Petri: en la Automàtica y la Informática.
AC/Thomson, (2002),
[Silva, 2006a]
Silva, M. (2006a). Discrete event systems and life cycle: A Petri nets-based view. In: Procs. of the Int. Mediterranean Multiconference, I3M2006 in: A. Bruzzone, A. Guasch, M. A. Piera y J. Rozenblit, (Eds.), Barcelona. pp. 5–12.
[Silva, 2006b]
M. Silva.
Terminología.
Revista Iberoamericana de Automática e Informática Industrial, 3 (2006), pp. 122-123
[Silva and Teruel, 1996]
M. Silva, E. Teruel.
A systems theory perspective of discrete event dynamic systems: The Petri net paradigm.
Symposium on Discrete Events and Manufacturing Systems. CESA ′96 IMACS Multiconference, pp. 1-12
[Silva and Teruel, 1998]
Silva, M. y E. Teruel (1998). DEDS along their life-cycle: interpreted extension of Petri nets. In: IEEE International Conference on Systems, Man and Cybernetics (SMC’98). IEEE. SAn Diego, USA.
[Silva and Recalde, 2002]
M. Silva, L. Recalde.
Petri nets and integrality relaxations: A view of continuous Petri nets.
IEEE Trans. on Systems, Man, and Cybernetics, 32 (2002), pp. 314-327
[Silva and Recalde, 2003]
M. Silva, L. Recalde.
Unforced continuous Petri nets and positive systems.
Positive Systems. Proceedings of the First Multidisciplinary International Symposium on Positive Systems: Theory and Applications (POSTA 2003), pp. 55-62
[Silva and Recalde, 2004]
M. Silva, L. Recalde.
On fluidification of Petri net models: from discrete to hybrid and continuous models.
Annual Reviews in Control, 28 (2004), pp. 253-266
[Silva et al., 1998]
M. Silva, E. Teruel, J.M. Colom.
Linear algebraic and linear programming techniques for the analysis of net systems.
Lectures in Petri Nets. I: Basic Models, pp. 309-373
[Sussmann and Willems, 1997]
H.J. Sussmann, J.C. Willems.
300 years of optimal control: from the brachystochrone to the maximum principle.
IEEE Control Systems Magazine, 17 (1997), pp. 32-44
[Turner et al., 2000]
M.C. Turner, I. Postlethwaite, D.J. Walker.
Non-linear tracking control for multi-variable constrained input linear systems.
International Journal of Control, 73 (2000), pp. 1160-1172
[Valk and Girault, 2003]
Petri Nets for Systems Engineering. A Guide to Modeling, Verification, and Applications,
[Xu et al., 2006]
Xu, J., L. Recalde y M. Silva (2006). Tracking control of join-free timed continuous Petri net systems. In: 2nd IFAC Conf. on Analysis and Design of Hybrid Systems, ADHS06. Alghero, Italy. pp. 30–36.
Los desarrollos presentados se han beneficiado en gran parte de los proyectos CICYT y FEDER DPI2003-06376 y DPI2006-15390, así como de la subvención del Gobierno de Aragón al GISED como Grupo de Excelencia en Investigación (2003–2007).
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