Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller
International Journal of Theoretical and Applied Mathematics
Volume 3, Issue 6, December 2017, Pages: 239-243
Received: Jun. 7, 2017;
Accepted: Jul. 24, 2017;
Published: Jan. 14, 2018
Views 2592 Downloads 127
Ying Shang, Department of Electrical and Computer Engineering, Southern Illinois University Edwardsville, Edwardsville, USA
This paper presents that the structural controllability and observability can be used for a class of discrete event systems modeled by industry-standard N-squared diagrams. The main results of this paper provide analytical assessment of large scale industrial system properties before the software simulation and hardware demonstration; therefore it offers immense savings in verification time and cost. The dynamics of N-squared diagrams are represented by linear time-invariant systems over the Boolean algebra. Structural controllability and structural observability of discrete event systems are transformed to “standard” controllability and observability problems in traditional linear systems over real numbers. The rank of the controllability and observability matrices determine not only the structural controllability and observability, but also which discrete nodes cannot be reached by the initial states and which discrete states have no outgoing paths to the output nodes, respectively. This rank condition is extremely easy to be verified through computer software, such as MATLAB, it can be used in large scale industrial systems or communication networks.
Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller, International Journal of Theoretical and Applied Mathematics.
Vol. 3, No. 6,
2017, pp. 239-243.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
J. Y. Le Boudec and P. Thiran, Network Calculus, John Wiley and Sons, Springer-Verlag, 2002.
C. G. Cassandras. Discrete Event Systems: Modeling and Performance Analysis. Irwinand Aksen, Boston, 1993.
P. M. Sain, Y. Shang, and M. K. Sain, “Reachability analysis for n-squared sate charts over a Boolean semiring applied to hysteretic discrete event structural control model”. Proceedings of American Control Conference, June 8-10, 2005.
P. Sain. “Qualitative results for a hierarchical discrete event control paradigm applied to structures operating under nominal and fault conditions,” Proceedings of American Control Conference, June 30-July 2, 2004.
F. Baccelli, G. Cohen, G. J. Olsder, and K. P. Quadrat. Synchronization and Linearity: An Algebra for discrete event systems, John Wiley and Sons, New York, 1992.
S. Zerhouni, P. Spacek, A. EL Moudni, and M. Ferney. “Max-plus algebra for discrete event systems-some links to structural controllability and structural observability,” In Proceedings of IEEE International Symposium on Intelligent Control, August 27-29, 1995.
K. Cai, R. Zhang, W. M. Wonham. Relative observability of discrete-event systems and its supremal sublanguages, IEEE Transactions on Automatica Control, Vol. 60, Issue 3, pp. 659-670, 2015.
H. Hihi, Structural Observability of Controlled Switching Linear Systems, International Journal of Control Science and Engineering, Vol. 2, Issue 5, pp. 127-135, 2012.
X. Yin, S. Lafortune, A general approach for synthesis of supervisors for partially-observed discrete-event systems, In Proceedings of the 19th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014.
S. Gracy, F. Garin, A. Y. Kibangou. Strong Structural Input and State Observability of LTV Network Systems with Multiple Unknown Inputs. In Proceedings of the 20th IFAC World Congress, Toulouse, France, July 9-14, 2017.
H. Ibrahim, P. Dague, A. Grastien, L. Ye, L. Simon, Diagnosability Planning for Controllable Discrete Event Systems, in Proceedings of Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, CA, USA, Feb. 4-9, 2017.