Observers Design for Discrete-Event Systems Modelled by S-Nets

Raul CAMPOS-RODRIGUEZ, Mildreth ALCARAZ-MEJIA
ITESO University,
Periferico Sur # 8585, Tlaquepaque, 45604, Mexico.
campos@iteso.mx, mildreth@iteso.mx

ABSTRACT: This paper addresses the design of observers for Discrete-Event Systems modelled by Output Petri nets. The observer is conceived as a copy of the system and a corrective term based on the execution trajectories. The observer performs a tracking of the transition sequence executed by the net. Based on this information, the observer is able to produce approximations of the initial and current state of the system. The focus is a subclass of Petri nets called S-Nets. A Lyapunov criterion is used for testing the stability of the herein proposed scheme. This criterion allows for proving that the observers are asymptotically stable and it supports characterizing the region of stability of the System/Observer pair, as well. An application example is developed through the paper to illustrate the results. Some graphs are provided to show the approximation error of the observer under different initial conditions.

KEYWORDS: Observer Design, Petri Nets, S-Nets, Discrete-Event Systems, Sequence Observer, Lyapunov Stability.

>>FULL TEXT: PDF

CITE THIS PAPER AS:
Raul CAMPOS-RODRIGUEZ, Mildreth ALCARAZ-MEJIA, Observers Design for Discrete-Event Systems Modelled by S-Nets, Studies in Informatics and Control, ISSN 1220-1766, vol. 26(1), pp. 13-22, 2017. https://doi.org/10.24846/v26i1y201702

REFERENCES

Campos-Rodriguez R. & Alcaraz-Mejia M. (2016). An Efficient Testing for the Detection of Trajectories in Discrete-Event Systems Modelled by S-Nets, Studies in Informatics and Control, 25 (3), 363-374.
Campos-Rodriguez R., Alcaraz-Mejia M & Sanchez-Ramirez U. (2016). Simulation of Discrete-Event Systems in MATLAB, Applications from Engineering with MATLAB Concepts, Assoc. Prof. Jan Valdman (Ed.), In Tech. DIO: 10. 5772/63230.
Campos-Rodriguez R. & Alcaraz-Mejia M. (2010). A Matlab/Simulink Framework for the Design of Controllers and Observers for Discrete-Event Systems, Electronics and Electrical Engineering, 99 (3), 63-68.
Campos-Rodriguez R., Ramirez-Trevino A. & Lopez-Mellado E. (2006), Observability Analysis of Free-Choice Petri Net Models, IEEE/SMC Intel. on System of Systems Engineering, 24-26.

Campos-Rodriguez R., Alcaraz-Mejia M. & Mireles-Garcia J. (2007), Supervisory Control of Discrete Event Systems Using Observers, Mediterranean Conf. on Control & Automation, (pp. 1-7).
Ramadge P. J. G. & Wonham W. M. (1989). The Control of Discrete Event Systems, of the IEEE, 77 (1), 81-98.
Kumar R. & Shayman M. A. (1998). Formulae relating controllability observability and co-observability, Automatica, 2 (1), 211-215.
Wong K. C. & Wonham W. M. (2004). On the Computation of Observers in Discrete-Event Systems, Discrete Event Dynamic Systems, 14 (1), 55-107.
Shaolong S. & Feng L. (2013). I-Detectability of Discrete-Event Systems, IEEE Trans. Autom. Sc. and Eng., 10 (1), 187-196.
Shu S. & Lin F. (2011). Generalized detectability for discrete event systems, Control Lett., 60 (5), 310–317.
Ozveren C. M. & Willsky A. S. (1990). Observability of discrete event dynamic systems, IEEE Trans. Autom. Control, 35 (7), 797-806.
Takai S., Ushio T. & Kodama S. (1995). Static-state feedback control of discrete-event systems under partial observation, IEEE Trans. Autom. Ctrl., 40 (11), 1950-1954.
Yong L. & Wonham W. M. (1994). Control of vector discrete-event systems. II: Controller Synthesis. IEEE Trans. Autom. Control, 39 (3), 512—531, 0018-9286.
Li Y. & Wonham W. M. (1993). Control of vector discrete-event systems I: The base model, IEEE Trans. Autom. Ctrl., 38 (8), 1214-1227.
Moody J. O. & Antsaklis P. J. (2000). Petri net supervisors for DES with uncontrollable and unobservable transitions. IEEE Trans. Autom. Control, 45 (3), 462-476.
Giua A. & Seatzu C. (2002). Observability of place/transition nets. IEEE Trans. Automatic Control, 47 (9), 1424-1437.
Ramirez-Trevino A., Rivera-Rangel I. & Lopez-Mellado E. (2003). Observability of discrete event systems modeled by interpreted petri nets. IEEE Trans. Robotics and Autom. 19 (4), 557-565.
Rivera-Rangel I., Ramírez-Treviño A., Aguirre-Salas L. & Ruiz-Leon J. (2005). Geometrical Characterization of Observability in Interpreted Petri Nets. Kybernetika. 41 (5), 553-574.
Desel J. & Esparza J. (2005). Free Choice Petri Nets. Cambridge University Press.
Hopcroft J. E. & Ullman J. D. (1979). Introduction to automata theory, languages, and computation. Addison-Wesley.
Passino, K. M. & Burguess, K. L. (1998). Stability Analysis of Discrete Event Systems. John Wiley & Sons.