Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller

Ying Shang

doi:doi:10.11648/j.ijtam.20170306.20

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Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller

Ying Shang

Published in International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 6)

Received: 7 June 2017 Accepted: 24 July 2017 Published: 14 January 2018

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Abstract

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.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.ijtam.20170306.20
Page(s)	239-243
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Discrete Event Systems, N 2 Diagram/Charts, Controllability, Observability

References

[1]	J. Y. Le Boudec and P. Thiran, Network Calculus, John Wiley and Sons, Springer-Verlag, 2002.
[2]	C. G. Cassandras. Discrete Event Systems: Modeling and Performance Analysis. Irwinand Aksen, Boston, 1993.
[3]	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.
[4]	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.
[5]	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.
[6]	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.
[7]	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.
[8]	H. Hihi, Structural Observability of Controlled Switching Linear Systems, International Journal of Control Science and Engineering, Vol. 2, Issue 5, pp. 127-135, 2012.
[9]	X. Yin, S. Lafortune, A general approach for synthesis of supervisors for partially-observed discrete-event systems, In Proceedings of the 19^th IFAC World Congress, Cape Town, South Africa, August 24-29, 2014.
[10]	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 20^th IFAC World Congress, Toulouse, France, July 9-14, 2017.
[11]	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.

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APA Style

Ying Shang. (2018). Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller. International Journal of Theoretical and Applied Mathematics, 3(6), 239-243. https://doi.org/10.11648/j.ijtam.20170306.20

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ACS Style

Ying Shang. Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller. Int. J. Theor. Appl. Math. 2018, 3(6), 239-243. doi: 10.11648/j.ijtam.20170306.20

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AMA Style

Ying Shang. Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller. Int J Theor Appl Math. 2018;3(6):239-243. doi: 10.11648/j.ijtam.20170306.20

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@article{10.11648/j.ijtam.20170306.20,
  author = {Ying Shang},
  title = {Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {239-243},
  doi = {10.11648/j.ijtam.20170306.20},
  url = {https://doi.org/10.11648/j.ijtam.20170306.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170306.20},
  abstract = {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.},
 year = {2018}
}

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TY  - JOUR
T1  - Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller
AU  - Ying Shang
Y1  - 2018/01/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ijtam.20170306.20
DO  - 10.11648/j.ijtam.20170306.20
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 239
EP  - 243
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170306.20
AB  - 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.
VL  - 3
IS  - 6
ER  -

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Author Information

Ying Shang

Department of Electrical and Computer Engineering, Southern Illinois University Edwardsville, Edwardsville, USA

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APA Style

Ying Shang. (2018). Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller. International Journal of Theoretical and Applied Mathematics, 3(6), 239-243. https://doi.org/10.11648/j.ijtam.20170306.20

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ACS Style

Ying Shang. Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller. Int. J. Theor. Appl. Math. 2018, 3(6), 239-243. doi: 10.11648/j.ijtam.20170306.20

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AMA Style

Ying Shang. Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller. Int J Theor Appl Math. 2018;3(6):239-243. doi: 10.11648/j.ijtam.20170306.20

Copy | Download

@article{10.11648/j.ijtam.20170306.20,
  author = {Ying Shang},
  title = {Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {3},
  number = {6},
  pages = {239-243},
  doi = {10.11648/j.ijtam.20170306.20},
  url = {https://doi.org/10.11648/j.ijtam.20170306.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20170306.20},
  abstract = {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.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Structural Controllability and Observability in Industrial N 2 State Charts Applied to a Supervisory Servo Controller
AU  - Ying Shang
Y1  - 2018/01/14
PY  - 2018
N1  - https://doi.org/10.11648/j.ijtam.20170306.20
DO  - 10.11648/j.ijtam.20170306.20
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 239
EP  - 243
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20170306.20
AB  - 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.
VL  - 3
IS  - 6
ER  -

Copy | Download