Skip to main content
SpringerLink
Log in

Integrated fault detection and control for two-dimensional Roesser systems

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper addresses the problem of integrated fault detection and control for two-dimensional (2-D) Roesser systems. A fault detection observer/controller is designed to detect faults in low-frequency domain and satisfy some control specifications simultaneously. By the generalized Kalman-Yakubovich-Popov (KYP) lemma and some useful lemmas, this design problem is formulated as a multiobjective optimization problem. A two-step algorithm is proposed to solve this non-convex problem. The effectiveness of the proposed algorithm is illustrated by a numerical example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. R. P. Roesser, “A discrete state-space model for linear image processing,” IEEE Trans. Automatic Contr., vol. 20, no. 1, pp. 1–10, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  2. E. Fornasini and G. Marchesini, “State-space realization theory of two-dimensional filters,” IEEE Trans. Automatic Contr., vol. 21, no. 4, pp. 484–492, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Kaczorek, Two-Dimensional Linear Systems, Springer-Verlag, Berlin, Germany, 1985.

    MATH  Google Scholar 

  4. C. Du and L. Xie, Control and Filtering of Two-Dimensional Systems, Springer-Verlag, Berlin, Germany, 2002.

    MATH  Google Scholar 

  5. M. Bisiacco and M. E. Valcher, “Observer-based fault detection and isolation for 2D state-space models,” Multidim. Syst. Sign. Process. vol. 17, pp. 219–242, 2006. [click]

    Article  MathSciNet  MATH  Google Scholar 

  6. M. Bisiacco and M. E. Valcher, “The general fault detection and isolation problem for 2D state-space models,” Systems & Control Letters, vol. 55, pp. 894–899, 2006. [click]

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Baniamerian, N. Meskin, and K. Khorasani, “Geometric fault detection and isolation of two-dimensional (2D) systems,” Proceedings of the American Control Conference, Washington, DC, USA, June 17-19, 2013.

    Google Scholar 

  8. L. Wu, X. Yao, and W. X. Zheng, “Generalized H 2 fault detection for two-dimensional Markovian jump systems,” Automatica, vol. 48, pp. 1741–1750, 2012. [click]

    Article  MathSciNet  MATH  Google Scholar 

  9. D.-W. Ding, H. Wang, and X. Li, “H −/H ∞ fault detection observer design for two-dimensional Roesser systems,” Systems & Control Letters, vol. 82, pp. 115–120, 2015. [click]

    Article  MathSciNet  MATH  Google Scholar 

  10. D.-W. Ding, X. Du and X. Li, “Finite-frequency model reduction of two-dimensional digital filters,” IEEE Transactions on Automatic Control, vol. 60, no. 6, pp. 1624–1629, 2015.

    Article  MathSciNet  Google Scholar 

  11. C. A. Jacobson and C. N. Nett, “An integrated approach to controls and diagnostics using the four parameter controller,” IEEE Trans. Control System Mag., vol. 11, no. 6, pp. 22–29, 1991.

    Article  Google Scholar 

  12. J. Stoustrup, M. Grimble, and H. H. Niemann, “Design of integrated systems for the control and detection of actuator/sensor faults,” Sensor Rev., vol. 17, no. 2, pp. 138–149, 1997. [click]

    Article  Google Scholar 

  13. M. J. Khosrowjerdi, R. Nikoukhah, and N. Safari-Shad, “A mixed H 2/H 1 approach to simultaneously fault detection and control,” Automatica, vol. 40, pp. 261–267, 2004. [click]

    Article  MathSciNet  MATH  Google Scholar 

  14. A. Marcos and G. J. Balas, “A robust integrated controller/diagnosis aircraft application,” Int. J. Robust Nonlinear Control, vol. 15, pp. 531–551, 2005. [click]

    Article  MathSciNet  MATH  Google Scholar 

  15. H. Wang and G.-H. Yang, “Simultaneous fault detection and control for uncertain linear discrete-time systems,” IET Control Theory & Applications, vol. 3, no. 5, pp. 583–594, 2009.

    Article  MathSciNet  Google Scholar 

  16. A. Fekih, “Fault-tolerant flight control design for effective and reliable aircraft systems,” Journal of Control and Decision vol. 1, no. 4, pp. 299–316, 2014. [click]

    Article  Google Scholar 

  17. G. Tao, “Direct adaptive actuator failure compensation control: a tutorial,” Journal of Control and Decision, vol. 1, no. 1, pp. 75–101, 2014. [click]

    Article  Google Scholar 

  18. H. Wang and G.-H. Yang, “A finite frequency domain approach to fault detection for linear discrete-time systems,” International Journal of Control, vol. 81, no. 7, pp. 1162–1171, 2008. [click]

    Article  MathSciNet  MATH  Google Scholar 

  19. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, PA, 1994.

    Book  MATH  Google Scholar 

  20. R. Yang, L. Xie, and C. Zhang, “Generalized twodimensional Kalman-Yakubovich-Popov lemma for discrete Roesser model,” IEEE Trans. Circuits Syst. I, vol. 55, no. 10, pp. 3223–3233, Nov. 2008.

    Article  MathSciNet  Google Scholar 

  21. A. Casavola, D. Famularo, and G. Franze, “Robust fault detection of uncertain linear systems via quasi-LMIs,” Automatica, vol. 44, pp. 289–295, 2008. [click]

    Article  MathSciNet  MATH  Google Scholar 

  22. X.-J. Li and G.-H. Yang, “Fault detection in finite frequency domains for multi-delay uncertain systems with application to ground vehicle,” Int. J. Robust Nonlinear Contr., vol. 25, no. 18, pp. 3780–3798, 2015.

    Article  MathSciNet  MATH  Google Scholar 

  23. C. Du and L. Xie, “Solutions for H ∞ filtering of twodimensional systems,” Multidimensional Systems and Signal Processing, vol. 11, pp. 301–320, 2000. [click]

    Article  MathSciNet  Google Scholar 

  24. M. C. De Olivera, J. C. Geromel and J. Bernussouz, “Extended H2 and H ∞ norm characterizations and controller parametrizations for discrete-time systems,” Int. J. Control, vol. 75, no. 9, 666-679, 2002. [click]

    Google Scholar 

  25. S. X. Ding, Model-Based Fault Diagnosis Techniques: Design Schemes, Algorithms, and Tools, Springer-Verlag, Berlin, Germany, 2008.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, P. R. China

    Yingying Ren & Da-Wei Ding

Authors
  1. Yingying Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Da-Wei Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Da-Wei Ding.

Additional information

Recommended by Associate Editor Guang-Hong Yang under the direction of Editor Duk-Sun Shim. This work was supported in part by National Natural Science of China under Grant 61473032, Beijing Natural Science Foundation under Grant 4153061, Program for New Century Excellent Talents in University under Grant NCET-13-0662, National Key Technologies R&D Program under Grant 2013BAB02B07, and the Fundamental Research Funds for the Central Universities under Grant FRF-TP-14-010C1.

Yingying Ren was born in Luyi, Henan Province, China, in 1994. She received her B.E. degree from Beijing Union University, Beijing, P. R. China, in 2014. She is currently a Master’s degree candidate in University of Science and Technology Beijing, Beijing, P. R. China. Her research interests include two-dimensional systems and fault detection.

Da-Wei Ding received his B.E. degree from the Ocean University of China, Qingdao, P. R. China, in 2003 and his Ph.D. degree in control theory and engineering from Northeastern University, Shenyang, P. R. China, in 2010. He is currently an Associate Professor with the School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, P. R. China. His research interests include robust control and filtering, fuzzy control, and multidimensional systems.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, Y., Ding, DW. Integrated fault detection and control for two-dimensional Roesser systems. Int. J. Control Autom. Syst. 15, 722–731 (2017). https://doi.org/10.1007/s12555-016-0215-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0215-3

Keywords

Search

Navigation