Article
Full entry |
PDF
(1.7 MB)
Feedback
PDF
(1.7 MB)
Feedback
Keywords:
synthesis problems; predictability; ARMA model; Dioid algebra; reachability of the objective
synthesis problems; predictability; ARMA model; Dioid algebra; reachability of the objective
Summary:
Processes modeled by a timed event graph may be represented by a linear model in dioïd algebra. The aim of this paper is to make temporal control synthesis when state vector is unknown. This information loss is compensated by the use of a simple model, the “ARMA” equations, which enables to introduce the concept of predictability. The comparison of the predictable output trajectory with the desired output determines the reachability of the objective.
References:
[1] Baccelli F., Cohen G., Olsder G. J., Quadrat J. P.: Synchronization and Linearity. An Algebra for Discrete Event Systems. Wiley, New York 1992 MR 1204266 | Zbl 0824.93003
[2] Bracker H.: Algorithms and Applications in Timed Discrete Event Systems. Ph.D thesis, Delft University of Technology, 1993
[3] Brat G. P., Garg V. K.: A max–plus algebra of signals for the supervisory control of real–time discrete event systems. In: 9th Symposium of the IFAC on Information Control in Manufacturing, Nancy–Metz 1998
[4] Cofer D. D., Garg V. K.: A timed model for the control of discrete event systems involving decisions in the max/plus algebra. In: Proc. 31st Conference on Decision and Control, Tucson 1992
[5] Cofer D. D.: Control and Analysis of Real–Time Discrete Event Systems. Ph.D. Thesis, University of Texas, Austin 1995
[6] Cofer D. D., Garg V. K.: Supervisory control of real–time discrete–event systems using lattice theory. IEEE Trans. Automat. Control 41 (1996), 2, 199–209 DOI 10.1109/9.481519 | MR 1375752 | Zbl 0846.93005
[7] Cohen G., Gaubert S., Quadrat J.-P.: From first to second–order theory of linear discrete event systems. In: 1st IFAC World Congress, Sydney 1993
[8] Declerck, Ph.: “ARMA” model and admissible trajectories in timed event graphs. In: CESA’96, IMACS, IEEE–SMC, Lille 1996
[9] Declerck, Ph.: Control synthesis using the state equations and the “ARMA” model in timed event graphs. In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997
[10] Declerck, Ph., Mares M.: Temporal control synthesis and failure recovery. In: 9th Symposium of the IFAC on Information Control in Manufacturing, Nancy–Metz 1998
[11] Gaubert S.: Théorie des systèmes linéaires dans les dioïdes. Ph.D Thesis, Ecole des Mines de Paris 1992
[12] Gazarik M. J., Kamen E. W.: Reachability and observability of linear systems over max–plus. In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997, revised version: Kybernetika 35 (1999), 2–12 MR 1705526
[13] Gondran M., Minoux M.: Graphes et algorithmes. Edition Eyrolles 1995 Zbl 1172.05001
[14] Prou J.-M., Wagneur E.: Controllability in the max–algebra. In: 5th IEEE Mediterranean Conference on Control and Systems, Paphos 1997, revised version: Kybernetika 35 (1999), 13–24 MR 1705527
Search
Partner of
