| Title:
|
Geometrical characterization of observability in Interpreted Petri Nets (English) |
| Author:
|
Rivera-Rangel, Israel |
| Author:
|
Ramírez-Treviño, Antonio |
| Author:
|
Aguirre-Salas, Luis I. |
| Author:
|
Ruiz-León, Javier |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
41 |
| Issue:
|
5 |
| Year:
|
2005 |
| Pages:
|
[553]-574 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work is concerned with observability in Discrete Event Systems (DES) modeled by Interpreted Petri Nets (IPN). Three major contributions are presented. First, a novel geometric characterization of observability based on input-output equivalence relations on the marking sequences sets is presented. Later, to show that this characterization is well posed, it is applied to linear continuous systems, leading to classical characterizations of observability for continuous systems. Finally, this paper translates the geometric characte-rization of observability into structural properties of the IPN. Thus, polynomial algorithms can be derived to check the observability in a broad class of IPN. (English) |
| Keyword:
|
discrete event systems |
| Keyword:
|
observability |
| Keyword:
|
Petri nets |
| MSC:
|
68Q85 |
| MSC:
|
93B07 |
| MSC:
|
93C65 |
| idZBL:
|
Zbl 1249.93126 |
| idMR:
|
MR2192423 |
| . |
| Date available:
|
2009-09-24T20:11:27Z |
| Last updated:
|
2015-03-23 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135678 |
| . |
| Reference:
|
[1] Aguirre-Salas L., Begovich, O., Ramírez-Treviño A.: Observability in interpreted Petri nets using sequence invariants.In: Proc. 41th IEEE Conference on Decision and Control, Hawai 2002, pp. 3602–3607 |
| Reference:
|
[2] Campos-Rodríguez R., Ramírez-Treviño, A., López-Mellado E.: Regulation control of partially observed discrete event systems.In: Proc. IEEE–SMC, The Hague 2004, pp. 1837–1842 |
| Reference:
|
[3] Chen C. T.: Linear System Theory and Design.Harcourt Brace Jovanovich Inc., New York 1970 |
| Reference:
|
[4] Cieslak R., Desclaux C., Fawaz, A., Varaiya P.: Supervisory control of discrete event processes with partial observation.IEEE Trans. Automat. Control 33 (1988), 249–260 10.1109/9.402 |
| Reference:
|
[5] Desel J., Esparza J.: Free Choice Petri Nets.Cambridge University Press, Cambridge 1995 Zbl 0836.68074, MR 1469221 |
| Reference:
|
[6] DiCesare F., Harhalakis G., Proth J. M., Silva, M., Vernadat F. B.: Practice of Petri Nets in Manufacturing.Chapman & Hall, London 1993 |
| Reference:
|
[7] Giua A.: Petri net state estimators based on event observation.In: Proc. 36th IEEE Conference on Decision and Control, San Diego 1997, pp. 4086–4091 |
| Reference:
|
[8] Giua A., Seatzu C.: Observability properties of Petri nets.In: Proc. 39th IEEE Conference on Decision and Control, Sydney 2000, pp. 2676–2681 |
| Reference:
|
[9] Hopcroft J. E., Ullman J. D.: Introduction to Automata Theory, Languages and Computation.Addison–Wesley, New York 1979 Zbl 0980.68066, MR 0645539 |
| Reference:
|
[10] Ichikawa A., Hiraishi K.: Analysis and Control of Discrete Event Systems Represented by Petri Nets.(Lecture Notes in Control and Inform. Sciences 103.) Springer, Berlin 1989, pp. 115–134 MR 0947968, 10.1007/BFb0042308 |
| Reference:
|
[11] Kumar R., Grag V. K., Marcus S. I.: On controllability and normality of discrete event dynamic systems.Systems Control Lett. 17 (1991), 157–168 MR 1125967, 10.1016/0167-6911(91)90061-I |
| Reference:
|
[12] Kumar R., Grag V. K., Marcus S. I.: On supervisory control of sequential behaviors.IEEE Trans. Automat. Control 37 (1992), 1978–1985 MR 1200617, 10.1109/9.182487 |
| Reference:
|
[13] Kumar R., Shayman M. A.: Formulae relating controllability, observability and co-observability.Automatica 2 (1998), 211–215 Zbl 0911.93020, MR 1609815, 10.1016/S0005-1098(97)00164-7 |
| Reference:
|
[14] Li Y., Wonham W. M.: Controllability and observability in the state-feedback control of discrete event systems.In: Proc. 27th IEEE Conference on Decision and Control, Austin 1988, pp. 203–207 |
| Reference:
|
[15] Lin F., Wonham W. M.: Decentralized control and coordination of discrete-event systems with partial observation.IEEE Trans. Automat. Control 35 (1990), 1330–1337 Zbl 0723.93043, MR 1078145, 10.1109/9.61009 |
| Reference:
|
[16] Meda M. E., Ramírez-Treviño, A., Malo A.: Identification in discrete event systems.IEEE Internat. Conference SMC, San Diego 1998, pp. 740–745 |
| Reference:
|
[17] Murata T.: Petri nets: properties, analysis and applications.Proc. IEEE 77 (1989), 541–580 |
| Reference:
|
[18] Özveren C. M., Willsky A. S.: Observability of discrete event dynamic systems.IEEE Trans. Automat. Control 35 (1990), 797–806 Zbl 0709.68030, MR 1058364, 10.1109/9.57018 |
| Reference:
|
[19] Perko L.: Differential Equations and Dynamic Systems.(Texts in Applied Mathematics.) Springer, New York 1996 10.1007/978-1-4684-0249-0 |
| Reference:
|
[20] Ramadge P. J.: Observability of discrete event systems.In: Proc. 25th IEEE Conference on Decision and Control, Athens 1986, pp. 1108–1112 |
| Reference:
|
[21] Ramírez-Treviño A., Rivera-Rangel, I., López-Mellado E.: Observability of discrete event systems modeled by interpreted Petri nets.IEEE Trans. Robotics and Automation 19 (2003), 557–565 10.1109/TRA.2003.814503 |
| Reference:
|
[22] Rivera-Rangel I., Aguirre-Salas L., Ramírez-Treviño, A., López-Mellado E.: Observer design for discrete event systems modeled by interpreted Petri nets.In: Proc. 39th IEEE Conference on Decision and Control, Sydney 2000, pp. 2260–2265 |
| Reference:
|
[23] Ushio T.: On the existence of finite-state supervisors under partial observations.IEEE Trans. Automat. Control 42 (1997), 1577–1581 Zbl 0891.93006, MR 1479096, 10.1109/9.649723 |
| Reference:
|
[24] Wonham W. M.: Linear Multivariable Control.A Geometric Approach. Springer, New York 1985 Zbl 0609.93001, MR 0770574 |
| . |
