Abstract
The classical partition of the event set into controllable and uncontrollable events from supervisory control theory is replaced by introducing the concept of control and observation cost of an event. This leads naturally to consider an optimal control problem for a given logical control specification. On the other hand, if we consider a timed model a performance optimization may be considered as well.
Here the case of generalized mutual exclusion constraint is considered for a Petri net plant. It has been shown that a constraint of this kind may be enforced via a monitor place. In this paper we propose an integer programming approach to synthesize the optimal monitor so as to minimize a given cost that represent a trade-off between the controller cost and cycle time of the closed loop net.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Basile, F., Chiacchio, P., and Giva, A. (2000). Petri net monitor design with control and observation costs. Proc. of the 39th IEEE Conference on Decision and Control, Sydney, AUS, pages 424–429.
Campos, J., Chiola, G., and Silva, M. (1991). Ergodicity and throughput bounds of petri nets with unique consistent firing count vector. IEEE Trans. On Computer Engineering, 17 (2): 117–125.
Campos, J., Chiola, G., and Silva, M. (1992). Properties and performance bounds for timed marked graphs. IEEE Trans. On Circuits and Systems-I: Fundamental Theory and Applications, 39 (5): 386–401.
Campos, J. and Silva, M. (1992). Structural tecniques and performance bounds of stocastic petri net models. In Advances in Petri Nets 1992, number 609 in LNCS, pages 352–391. Springer Verlag, Berlin.
Giva, A., DiCesare, F., and Silva, M. (1992). Generalized mutual exclusion constraints on nets with uncontrollable transitions. Proc. 1992 IEEE Int. Conf. on Systems, Man, and Cybernetics, Chigago, pages 974–979.
Krogh, B. H. and Holloway, L. E. (1991). Synthesis of feedback control logic for discrete manufacturing systems. Automatica, 27 (4): 614–651.
Li, Y. and Wonham, W. M. (1994). Control of vector discrete-event systems II–controller synthesis. IEEE Trans. on Automatic Control, 39 (3): 512–531.
Moody, J. O., Lemmon, M. D., and Antsaklis, P. (1996a). Supervisory control of petri nets with uncontrollable/unobservable transitions. 35th IEEE Conf. on Decision and Control, Kobe, Japan.
Moody, J. O., Yamalidou, K., Lemmon, M. D., and Antsaklis, P. (1996b). Feedback control of petri nets based on place invariants. Automatica, 32 (1): 15–28.
Murata, T. (1989). Petri nets: properties, analysis and applications. Proc. IEEE, 77 (4): 541–580.
Ramadge, P. J. and Wonham, W. M. (1989). Control of discrete-event systems. Proc. of the IEEE, 77 (1): 81–98.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Basile, F., Chiacchio, P., Giua, A. (2002). Optimal Petri Net Monitor Design. In: Caillaud, B., Darondeau, P., Lavagno, L., Xie, X. (eds) Synthesis and Control of Discrete Event Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6656-1_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-6656-1_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4942-4
Online ISBN: 978-1-4757-6656-1
eBook Packages: Springer Book Archive