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Descriptor Observers for Robust Fault Reconstruction in a Class of Nonlinear Descriptor Systems

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  • Control Theory and Applications
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Abstract

This paper presents a robust fault reconstruction scheme for a class of nonlinear descriptor systems that is affected by disturbances. The fault enters the system both linearly and through nonlinear functions in both the state and output equations. The system is first re-expressed into a form which is easier to manipulate. Two cases are considered: in the first case, the fault is present in the nonlinear function of the output equation, whereas in the second case, the nonlinear function of the output equation does not contain the fault. In each case, a nonlinear descriptor observer is used to reconstruct the fault, where the gains of the observer are designed using linear matrix inequalities such that the effect of disturbances on the fault reconstruction is bounded. As a result of their structure, the proposed descriptor observers do not require restrictions on the rates of the input and disturbances (unlike in observers using a state-space structure) which makes the proposed observers more widely applicable. Finally, two simulation examples are performed to verify the performance of the proposed observers.

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References

  1. W. Zheng, Z. Zhang, H. B. Wang, and M. Q. Zhang, “Quantized sliding mode H∞ control for singular Markovian jump systems with sensor failure and randomly changing structure,” International Journal of Control, Automation, and Systems, vol. 19, no. 12, pp. 3890–3902, 2021.

    Article  Google Scholar 

  2. S. Xu and J. Lam, Robust Control and Filtering of Singular Systems, Springer-Verlag, Berlin/Heidelberg, 2006.

    MATH  Google Scholar 

  3. J. Zhou, Q. Zhang, B. Men, and S. Huang, “Input-to-state stability of a class of descriptor systems,” International Journal of Robust and Nonlinear Control, vol. 24, no. 1, pp. 97–109, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  4. Y. Wang, V. Puig, F. Xu, and G. Cembrano, “Robust fault detection and isolation based on zonotopic unknown input observers for discrete-time descriptor systems,” Journal of the Franklin Institute, vol. 356, no. 10, pp. 5293–5314, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Li, Q. Zhang, X. G. Yan, and S. K. Spurgeon, “Observer-based fuzzy integral sliding mode control for nonlinear descriptor systems,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 5, pp. 2818–2832, 2018.

    Article  Google Scholar 

  6. X. Li, C. K. Ahn, D. Lu, and S. Guo, “Robust simultaneous fault estimation and nonfragile output feedback fault-tolerant control for Markovian jump systems,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 49, no. 9, pp. 1769–1776, 2019.

    Article  Google Scholar 

  7. T. H. Lee, C. P. Lim, S. Nahavandi, and R. G. Roberts, “Observer-based fault-tolerant control for linear systems with sensor and actuator faults,” IEEE Systems Journal, vol. 13, no. 2, pp. 1981–1990, 2019.

    Article  Google Scholar 

  8. C. Deng, X. Z. Jin, W. W. Che, and H. Wang, “Learning-based distributed resilient fault-tolerant control method for heterogeneous MASs under unknown leader dynamic,” IEEE Transactions on Neural Networks and Learning Systems, vol. 33, no. 10, pp. 5504–5513, 2022.

    Article  MathSciNet  Google Scholar 

  9. F. Zhu, Y. Shan, and Y. Tang, “Actuator and sensor fault detection and isolation for uncertain switched nonlinear system based on sliding mode observers,” International Journal of Control, Automation, and Systems, vol. 19, no. 9, pp. 3075–3086, 2021.

    Article  Google Scholar 

  10. W. S. Chua, J. C. L. Chan, C. P. Tan, E. K. P. Chong, and S. Saha, “Robust fault reconstruction for a class of nonlinear systems,” Automatica, vol. 113, 108718, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Laghrouche, J. Liu, F. S. Ahmed, M. Harmouche, and M. Wack, “Adaptive second-order sliding mode observer-based fault reconstruction for PEM fuel cell air-feed system,” IEEE Transactions on Control Systems Technology, vol. 23, no. 3, pp. 1098–1109, 2015.

    Article  Google Scholar 

  12. Y. Gao, J. Liu, G. Sun, M. Liu, and L. Wu, “Fault deviation estimation and integral sliding mode control design for Lipschitz nonlinear systems,” Systems & Control Letters, vol. 123, pp. 8–15, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  13. R. Shahnazi and Q. Zhao, “Adaptive fuzzy descriptor sliding mode observer-based sensor fault estimation for uncertain nonlinear systems,” Asian Journal of Control, vol. 18, no. 4, pp. 1478–1488, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  14. J. Cheng, J. H. Park, and Z. G. Wu, “Observer-based asynchronous control of nonlinear systems with dynamic event-based try-one-discard protocol,” IEEE Transactions on Cybernetics, pp. 1–11, 2021. DOI: https://doi.org/10.1109/TCYB.2021.3104806

  15. J. C. L. Chan, T. H. Lee, and C. P. Tan, “A sliding mode observer for robust fault reconstruction in a class of nonlinear non-infinitely observable descriptor systems,” Nonlinear Dynamics, vol. 101, no. 2, pp. 1023–1036, 2020.

    Article  Google Scholar 

  16. S. A. Nugroho, V. Hoang, M. Radosz, S. Wang, and A. F. Taha, “New insights on one-sided Lipschitz and quadratically-inner bounded nonlinear dynamic systems,” Proc. of the American Control Conference, pp. 4558–4563, 2020.

  17. J. Li, Y. Liu, J. Yu, Y. Sun, and M. Liu, “A new result of terminal sliding mode finite-time state and fault estimation for a class of descriptor switched systems,” Applied Mathematics and Computation, vol. 402, 126085, 2021.

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Li, J. Xia, J. Zhao, H. Zhang, and H. Shen, “Event-triggered extended dissipative control for networked singular systems,” International Journal of Control, Automation, and Systems, vol. 19, no. 1, pp. 382–391, 2021.

    Article  Google Scholar 

  19. J. C. L. Chan, T. H. Lee, and C. P. Tan, “Observer-based fault-tolerant control for non-infinitely observable descriptor systems,” in: J. H. Park (Ed.), Recent Advances in Control Problems of Dynamical Systems and Networks, Springer, Cham, pp. 123–145, 2021.

    Chapter  Google Scholar 

  20. Z. Gao and S. X. Ding, “Fault estimation and fault-tolerant control for descriptor systems via proportional, multiple-integral and derivative observer design,” IET Control Theory & Applications, vol. 1, no. 5, pp. 1208–1218, 2007.

    Article  MathSciNet  Google Scholar 

  21. T. Binazadeh and M. S. Asadinia, “A delay-dependent approach to finite-time H∞ control of nonlinear descriptor systems with state delay via observer-based control,” Circuits, Systems, and Signal Processing, vol. 39, no. 11, pp. 5454–5474, 2020.

    Article  Google Scholar 

  22. M. C. Nguyen, H. Trinh, and P. T. Nam, “Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities,” IMA Journal of Mathematical Control and Information, vol. 34, no. 3, pp. 919–935, 2017.

    MathSciNet  MATH  Google Scholar 

  23. T. Berger, “On observers for nonlinear differential-algebraic systems,” IEEE Transactions on Automatic Control, vol. 64, no. 5, pp. 2150–2157, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  24. S. Liu, X. Li, H. Wang, and J. Yan, “Adaptive fault estimation for T-S fuzzy systems with unmeasurable premise variables,” Advances in Difference Equations, vol. 2018, no. 1, pp. 105–117, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  25. F. Nemati, S. H. S. Mostafa, and A. Zemouche, “A nonlinear observer-based approach to fault detection, isolation and estimation for satellite formation flight application,” Automatica, vol. 107, pp. 474–482, 2019.

    Article  MathSciNet  MATH  Google Scholar 

  26. A. H. Tahoun and M. Arafa, “A new unmatched-disturbances compensation and fault-tolerant control for partially known nonlinear singular systems,” ISA Transactions, vol. 104, pp. 310–320, 2020.

    Article  Google Scholar 

  27. B. Jiang and F. N. Chowdhury, “Parameter fault detection and estimation of a class of nonlinear systems using observers,” Journal of the Franklin Institute, vol. 342, no. 7, pp. 725–736, 2005.

    Article  MathSciNet  MATH  Google Scholar 

  28. C. Martínez-García, C. Astorga-Zaragoza, V. Puig, J. Reyes-Reyes, and F. López-Estrada, “A simple nonlinear observer for state and unknown input estimation: DC motor applications,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 67, no. 4, pp. 710–714, 2020.

    Google Scholar 

  29. A. Sassi, H. S. Ali, M. Zasadzinski, and K. Abderrahim, “Adaptive observer design for a class of descriptor nonlinear systems,” European Journal of Control, vol. 44, pp. 90–102, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  30. H. Kazemi and A. Yazdizadeh, “Optimal state estimation and fault diagnosis for a class of nonlinear systems,” IEEE/CAA Journal of Automatica Sinica, vol. 7, no. 2, pp. 517–526, 2020.

    Article  MathSciNet  MATH  Google Scholar 

  31. Q. Ha and H. Trinh, “State and input simultaneous estimation for a class of nonlinear systems,” Automatica, vol. 40, no. 10, pp. 1779–1785, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  32. J. Pan, M. Meng, and J. Feng, “A note on observers design for one-sided Lipschitz nonlinear systems,” Proc. of the 34th Chinese Control Conference, pp. 1003–1007, 2015.

  33. J. C. L. Chan, T. H. Lee, C. P. Tan, H. Trinh, and J. H. Park, “A nonlinear observer for robust fault reconstruction in one-sided Lipschitz and quadratically inner-bounded nonlinear descriptor systems,” IEEE Access, vol. 9, pp. 22455–22469, 2021.

    Article  Google Scholar 

  34. D. Kharrat, H. Gassara, A. El Hajjaji, and M. Chaabane, “Adaptive observer and fault tolerant control for Takagi-Sugeno descriptor nonlinear systems with sensor and actuator faults,” International Journal of Control, Automation, and Systems, vol. 16, no. 3, pp. 972–982, 2018.

    Article  MATH  Google Scholar 

  35. D. Du, Y. Yang, H. Zhao, and Y. Tan, “Robust fault diagnosis observer design for uncertain switched systems,” International Journal of Control, Automation, and Systems, vol. 18, no. 12, pp. 3159–3166, 2020.

    Article  Google Scholar 

  36. L. Dai, Singular Control Systems, Springer-Verlag, Berlin, 1989.

    Book  MATH  Google Scholar 

  37. W. Zhang, Y. Zhao, and L. Sheng, “Some remarks on stability of stochastic singular systems with state-dependent noise,” Automatica, vol. 51, pp. 279–277, 2015.

    Article  MathSciNet  Google Scholar 

  38. J. Li and Q. Zhang, “An integral sliding mode control approach to observer-based stabilization of stochastic Itô descriptor systems,” Neurocomputing, vol. 173, no. 3, pp. 1330–1340, 2016.

    Article  Google Scholar 

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Authors and Affiliations

  1. Division of Electronic Engineering, Jeonbuk National University, Jeonju, 54896, Korea

    Joseph Chang Lun Chan & Tae H. Lee

  2. Selangor Human Resource Development Centre, Shah Alam, 40100, Malaysia

    Wen-Shyan Chua

  3. Advanced Engineering Platform, Monash University Malaysia, Bandar Sunway, 47500, Malaysia

    Chee Pin Tan

  4. School of Engineering, Monash University Malaysia, Bandar Sunway, 47500, Malaysia

    Joseph Chang Lun Chan, Wen-Shyan Chua & Chee Pin Tan

Authors
  1. Joseph Chang Lun Chan
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  2. Wen-Shyan Chua
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  4. Chee Pin Tan
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Correspondence to Tae H. Lee.

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This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2020R1C1C1012707) and also was supported by National University Development Project in 2020.

Joseph Chang Lun Chan received his B.Eng. (Hons.) and Ph.D. degrees from Monash University Malaysia, in 2013 and 2019, respectively. He was a postdoctoral researcher from 2019 to 2021 in Jeonbuk National University, Korea, where he was also a Brain Korea Plus (BK21+) Postdoctoral Fellowship Scholar. Since 2021, he has been a postdoctoral research fellow in Monash University Malaysia. His research focusses on application of sliding mode observers in non-infinitely observable descriptor systems and other practical systems, as well as fault reconstruction in non-linear systems.

Wen-Shyan Chua obtained his Ph.D. degree in control systems engineering and a B.Eng. degree in mechatronics engineering from Monash University Malaysia and is a registered Professional Technologist under the Malaysian Board of Technologists (MBOT). He is currently the Head of Malaysian Smart Factory 4.0 @ Selangor Human Resource Development Centre (SHRDC) which is a recognized technology centre by the Malaysian Productivity Corporation (MPC) to support and accelerate Industry 4.0 technology adoption within the Malaysian Industries. He currently focuses on developing community-driven and open-source technology integration and use cases to boost adoption of Industry 4.0 within the industries and community in Malaysia.

Tae H. Lee received his B.S., M.S., and Ph.D. degrees in electrical engineering from Yeungnam University, Korea, in 2009, 2011, and 2015, respectively. He was a postdoctoral researcher in the same university from 2015 to 2017 and a Alfred Deakin Postdoctoral Research Fellow at Institute for Intelligent Systems Research and Innovation, Deakin University, Australia in 2017. He began with Jeonbuk National University, Korea in 2017, where he is currently an Associate Professor. His research interests are in the field of stability analysis, sampleddata control, dynamics of systems, and control issues in network systems. He is an author/coauthor of several journal papers and books. Dr. Lee currently serves as an Associate Editor for the Applied Mathematics and Computation.

Chee Pin Tan received his B.Eng. (Hons.) and Ph.D. degrees from University of Leicester, Leicester, UK, in 1998 and 2002, respectively. He is currently a Professor at the School of Engineering, Monash University Malaysia, Bandar Sunway, Malaysia. He has authored more than 60 internationally peer-reviewed research articles, including a book on fault reconstruction. His research interests include robust fault estimation and observers. He is currently an Associate Editor of the Journal of the Franklin Institute and the International Journal of Systems Science.

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Chan, J.C.L., Chua, WS., Lee, T.H. et al. Descriptor Observers for Robust Fault Reconstruction in a Class of Nonlinear Descriptor Systems. Int. J. Control Autom. Syst. 21, 697–710 (2023). https://doi.org/10.1007/s12555-022-0180-y

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  • DOI: https://doi.org/10.1007/s12555-022-0180-y

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