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Robust Fault Estimation and Accommodation for a Class of T–S Fuzzy Systems with Local Nonlinear Models

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Abstract

This paper focuses on the problems of fault estimation and accommodation for a class of T–S fuzzy systems with local nonlinear models and having an external disturbance and sensor and actuator faults, simultaneously. A fuzzy robust fault estimation observer is designed to estimate the system state and sensor and actuator faults. Compared with existing results, the observer not only is robust to the disturbance but also has a wider application range and more freedom for design. To compensate for the effect of faults and to stabilize the closed-loop system, an observer-based fault-tolerant controller is proposed. The separate design of the observer and controller avoids coupling between them. Finally, a simulation is conducted to demonstrate the effectiveness of the proposed method.

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References

  1. S. Aouaouda, M. Chadli, V. Cocquempot, M.T. Khadir, Multi-objective \(H_-/H_\infty \) fault detection observer design for Takagi–Sugeno fuzzy systems with unmeasurable premise variables: descriptor approach. Int. J. Adapt. Control Signal Process. 350(9), 2627–2645 (2013)

    MathSciNet  MATH  Google Scholar 

  2. S. Aouaouda, M. Chadli, H.R. Karimi, Robust static output-feedback controller design against sensor failure for vehicle dynamics. IET Control Theory Appl. 8(9), 728–737 (2014)

    Article  MathSciNet  Google Scholar 

  3. S. Aouaouda, M. Chadli, M.T. Khadir, T. Bouarar, Robust fault tolerant tracking controller design for unknown inputs T–S models with unmeasurable premise variables. J. Process Control 22(5), 719–725 (2012)

    Article  Google Scholar 

  4. S. Aouaouda, M. Chadli, P. Shi, H.R. Karimi, Discrete-time \(H_-/H_\infty \) sensor fault detection observer design for nonlinear systems with parameter uncertainty. Int. J. Robust Nonlinear Control 25(3), 339–361 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki, Diagnosis and Fault-Tolerant Control (Springer, Secaucus, 2006)

    MATH  Google Scholar 

  6. M. Chadli, A. Abdo, S.X. Ding, \(H_-/H_\infty \) fault detection filter design for discrete-time Takagi–Sugeno fuzzy system. Automatica 49(7), 1996–2005 (2013)

    Article  MathSciNet  Google Scholar 

  7. M. Chadli, S. Aouaouda, H.R. Karimi, P. shi, Robust fault tolerant tracking controller design for a VTOL aircraft. J. Frankl. Inst. 350(9), 2627–2645 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. J. Chen, R.J. Patton, Robust Model-Based Fault Diagnosis for Dynamic Systems (Kluwer, Norwell, 1999)

    Book  MATH  Google Scholar 

  9. T.V. Dang, W.J. Wang, L. Luoh, C.H. Sun, Adaptive observer design for the uncertain Takagi–Sugeno fuzzy system with output disturbance. IET Control Theory Appl. 6(10), 1351–1366 (2011)

    Article  MathSciNet  Google Scholar 

  10. S.X. Ding, Model-based fault diagnosis techniques: desig schemes, algorithms, and tools (Springer, Berlin, 2008)

    Google Scholar 

  11. J.X. Dong, Y.Y. Wang, G.H. Yang, \(H_\infty \) and mixed \(H_2/H_\infty \) control of discrete-time T–S fuzzy systems with local nonlinear models. Fuzzy Sets Syst. 164(1), 1–24 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. J.X. Dong, Y.Y. Wang, G.H. Yang, Control synthesis of continuous-time T–S fuzzy systems with local nonlinear models. IEEE Trans. Syst. Man Cybern. Part B Cybern. 39(5), 1245–1258 (2009)

    Article  Google Scholar 

  13. Z.W. Gao, S.X. Ding, Fault reconstruction for Lipschitz nonlinear descriptor systems via linear matrix inequality approach. Circuits Syst. Signal Process. 27(3), 295–308 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Z.W. Gao, X. Shi, S.X. Ding, Fuzzy state/disturbance observer design for T–S fuzzy systems with application to sensor fault estimation. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(3), 875–880 (2008)

    Article  Google Scholar 

  15. H. Ghorbel, A.E. Hajjaji, M. Souissi, M. Chaabane, Fault-tolerant trajectory tracking control for Takagi–Sugeno systems with unmeasurable premise variables: descriptor approach. Circuits Syst. Signal Process. 33(6), 1763–1781 (2014)

    Article  MathSciNet  Google Scholar 

  16. J. Han, H.G. Zhang, Y.C. Wang, Y. Liu, Disturbance observer based fault estimation and dynamic output feedback fault tolerant control for fuzzy systems with local nonlinear models. ISA Trans. doi:10.1016/j.isatra.2015.08.015

  17. H. Hu, B. Jiang, H. Yang, Robust fault-tolerant control for uncertain delta operator switched systems. IET Control Theory Appl. 8(2), 120–130 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  18. Z.G. Hu, G.R. Zhao, L. Zhang, D.W. Zhou, Fault estimation for nonlinear dynamic system based on the second-order sliding mode observer. Circuits Syst. Signal Process. doi:10.1007/s00034-015-0060-2

  19. B. Jiang, F.N. Chowdhury, Fault estimation and accommodation for linear MIMO discrete-time systems. IEEE Trans. Control Syst. Technol. 13(3), 493–499 (2005)

    Article  Google Scholar 

  20. B. Jiang, K. Zhang, P. Shi, Integrated fault estimation and accommodation design for discrete-time Takagi-Sugeno fuzzy systems with actuator faults. IEEE Trans. Fuzzy Syst. 19(2), 291–304 (2011)

    Article  Google Scholar 

  21. E. Kamal, A. Aitouche, D. Abbes, Robust fuzzy scheduler fault tolerant control of wind energy systems subject to sensor and actuator faults. Int. J. Electr. Power Energy Syst. 55, 402–419 (2014)

    Article  Google Scholar 

  22. H.Y. Li, Y.N. Pan, Q. Zhou, Filter design for interval type-2 fuzzy systems with \(D\) stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2015)

    Article  Google Scholar 

  23. H.Y. Li, X.J. Sun, L.G. Wu, H.K. Lam, State and output feedback control of a class of fuzzy systems with mismatched membership functions. IEEE Trans. Fuzzy Syst. doi:10.1109/TFUZZ.2014.2387876

  24. H.Y. Li, C.W. Wu, P. Shi, Y.B. Gao, Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. 45(11), 2378–2389 (2015)

    Article  Google Scholar 

  25. H.Y. Li, C.W. Wu, L.G. Wu, H.K. Lam, Y.B. Gao, Filtering of interval type-2 fuzzy systems with intermittent measurements. IEEE Trans. Cybern. doi:10.1109/TCYB.2015.2413134

  26. X.J. Li, G.H. Yang, Fault detection for T–S fuzzy systems with unknown membership functions. IEEE Trans. Fuzzy Syst. 22(1), 139–152 (2013)

    Article  Google Scholar 

  27. M. Liu, X. Cao, P. Shi, Fuzzy-model-based fault-tolerant design for nonlinear stochastic systems against simultaneous sensor and actuator faults. IEEE Trans. Fuzzy Syst. 21(5), 789–799 (2013)

    Article  Google Scholar 

  28. A. Manivannan, S. Muralisankar, Robust stability analysis of Takagi–Sugeno fuzzy nonlinear singular systems with time-varying delays using delay decomposition approach. Circuits Syst. Signal Process. doi:10.1007/s00034-015-0096-3

  29. H. Moodi, M. Farrokhi, On observer-based controller design for Sugeno systems with unmeasurable premise variables. ISA Trans. 53(2), 305–316 (2014)

    Article  Google Scholar 

  30. J.Q. Qiu, M.F. Ren, Y.R. Niu, Y.C. Zhao, Y.M. Guo, Fault estimation for nonlinear dynamic systems. Circuits Syst. Signal Process. 31(2), 555–564 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  31. R. Sakthivel, K. Sundareswari, K. Mathiyalagan, S. Santra, Reliable \(H_\infty \) stabilization of fuzzy systems with random delay via nonlinear retarded control. Circuits Syst. Signal Process. doi:10.1007/s00034-015-0115-4

  32. M. Sami, R.J. Patton, Active fault tolerant control for nonlinear systems with simultaneous actuator and sensor faults. Int. J. Control Autom. Syst. 11(6), 1149–1161 (2013)

    Article  Google Scholar 

  33. Q.K. Shen, B. Jiang, P. Shi, Adaptive fault diagnosis for T–S fuzzy systems with sensor faults and system performance analysis. IEEE Trans. Fuzzy Syst. 22(2), 274–285 (2014)

    Article  Google Scholar 

  34. C. Sun, F.L. Wang, X.Q. He, Robust fault estimation for Takagi–Sugeno nonlinear systems with time-varying state delay. Circuits Syst. Signal Process. 34(2), 641–661 (2015)

    Article  MathSciNet  Google Scholar 

  35. K. Tanaka, H.O. Wang, Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach (Wiley, New York, 2001)

    Book  Google Scholar 

  36. H. Tuan, P. Apkarian, T. Narikiyo, Y. Yamamoto, Parameterized linear matrix inequality techniques in fuzzy control system design. IEEE Trans. Fuzzy Syst. 9(2), 324–332 (2001)

    Article  Google Scholar 

  37. H.M. Wang, D. Ye, G.H. Yang, Actuator fault diagnosis for uncertain T–S fuzzy systems with local nonlinear models. Nonlinear Dyn. 76(4), 1977–1988 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  38. Q. Wen, R. Kumar, J. Huang, Framework for optimal fault-tolerant control synthesis: maximize prefault while minimize post-fault behaviors. IEEE Trans. Syst. Man Cybern. Syst. 44(8), 1056–1066 (2014)

    Article  Google Scholar 

  39. X.P. Xie, D. Yue, T.D. Ma, X.L. Zhu, Further studies on control synthesis of discrete-time T–S fuzzy systems via augmented multi-indexed matrix approach. IEEE Trans. Cybern. 44(12), 2784–2791 (2014)

    Article  Google Scholar 

  40. X.P. Xie, D. Yue, X.L. Zhu, Further studies on control synthesis of discrete-time T–S fuzzy systems via useful matrix equalities. IEEE Trans. Fuzzy Syst. 22(4), 1026–1031 (2014)

    Article  Google Scholar 

  41. Y.Y. Xu, S.C. Tong, Y.M. Li, Prescribed performance fuzzy adaptive fault-tolerant control of non-linear systems with actuator faults. IET Control Theory Appl. 8(6), 420–431 (2014)

    Article  MathSciNet  Google Scholar 

  42. F.S. Yang, H.G. Zhang, G.T. Hui, S.Q. Wang, Mode-independent fuzzy fault-tolerant variable sampling stabilization of nonlinear networked systems with both time-varying and random delays. Fuzzy Sets Syst. 207, 45–63 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  43. F.S. Yang, H.G. Zhang, B. Jiang, X.D. Liu, Adaptive reconfigurable control of systems with time-varying delay against unknown actuator faults. Int. J. Adapt. Control Signal Process. 28(11), 1206–1226 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  44. H. Yang, B. Jiang, V. Cocquempot, Stabilization of Switched Nonlinear Systems with Unstable Modes (Springer, Switzerland, 2014)

    Book  MATH  Google Scholar 

  45. H. Yang, B. Jiang, M. Staroswiecki, Observer-based fault-tolerant control for a class of switched nonlinear systems. IET Control Theory Appl. 1(5), 1523–1532 (2007)

    Article  MathSciNet  Google Scholar 

  46. H.J. Yang, X. Li, Z.X. Liu, C.C. Hua, Fault detection for uncertain fuzzy systems based on the delta operator approach. Circuits Syst. Signal Process. 33(3), 733–759 (2014)

    Article  MathSciNet  Google Scholar 

  47. H.G. Zhang, Y.C. Wang, D.R. Liu, Delay-dependent guaranteed cost control for uncertain Stochastic fuzzy systems with multiple tire delays. IEEE Trans. Syst. Man Cybern. Part B Cybern. 38(1), 126–140 (2008)

    Article  Google Scholar 

  48. H.G. Zhang, X.P. Xie, Relaxed stability conditions for continuous-time T–S fuzzy-control systems via augmented multi-indexed matrix approach. IEEE Trans. Fuzzy Syst. 19(3), 478–492 (2011)

    Article  Google Scholar 

  49. K. Zhang, B. Jiang, P. Shi, Observer-based fault estimation and accomodation for dynamic systems (Springer, Berlin, 2013)

    Book  Google Scholar 

  50. X.D. Zhang, Matrix Analysis and Applications (Tsinghua University Press, Beijing, 2004)

    Google Scholar 

  51. Y.W. Zhang, N. Yang, S.P. Li, Fault isolation of nonlinear processes based on fault directions and features. IEEE Trans. Control Syst. Technol. 22(4), 1567–1572 (2014)

    Article  Google Scholar 

  52. J. Zhao, B. Jiang, P. Shi, H.T. Liu, Adaptive dynamic sliding mode control for near space vehicles under actuator faults. Circuits Syst. Signal Process. 32(5), 2281–2296 (2013)

    Article  MathSciNet  Google Scholar 

  53. G.M. Zhuang, X.J. Yu, J. Chen, Fault detection filtering for uncertain Itô stochastic fuzzy systems with time-varying delays. Circuits Syst. Signal Process. 34(9), 2839–2871 (2015)

    Article  MathSciNet  Google Scholar 

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (61433004, 61273027), and Liaoning Province Science and Technology Key Project(2013219005) and IAPI Fundamental Research Funds 2013ZCX14. This work was supported also by the development project of Key Laboratory of Liaoning Province.

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Correspondence to Huaguang Zhang.

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Han, J., Zhang, H., Wang, Y. et al. Robust Fault Estimation and Accommodation for a Class of T–S Fuzzy Systems with Local Nonlinear Models. Circuits Syst Signal Process 35, 3506–3530 (2016). https://doi.org/10.1007/s00034-015-0219-x

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