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A New Approach to Observer-Based Fault-Tolerant Controller Design for Takagi-Sugeno Fuzzy Systems with State Delay

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Abstract

This paper deals with the problem of active fault-tolerant control (FTC) for time-delay Takagi-Sugeno (T-S) fuzzy systems based on a fuzzy adaptive fault diagnosis observer (AFDO). A novel fuzzy fast adaptive fault estimation (FAFE) algorithm for T-S fuzzy models is proposed to enhance the performance of fault estimation, and sufficient conditions for the existence of the fault estimator are given in terms of linear matrix inequalities (LMIs). Using the obtained on-line fault estimation information, an observer-based fast active fault-tolerant controller is designed to compensate for the effect of faults by stabilizing the closed-loop system. Simulation results of a track trail system and a nonlinear numerical example are presented to illustrate the effectiveness of the proposed method.

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References

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

    MATH  Google Scholar 

  2. Y.Y. Cao, P.M. Frank, Stability analysis and synthesis of nonlinear time-delay systems via linear Takagi-Sugeno fuzzy models. Fuzzy Sets Syst. 124(2), 213–229 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Chen, R.J. Patton, Robust Model-based Fault Diagnosis for Dynamic Systems (Kluwer Academic, Norwell, 1999)

    MATH  Google Scholar 

  4. W. Chen, M. Saif, An iterative learning observer for fault detection and accommodation in nonlinear time-delay systems. Int. J. Robust Nonlinear Control 16(1), 1–19 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  5. B. Chen, X. Liu, S. Tong, Delay-dependent stability analysis and control synthesis of fuzzy dynamic systems with time delay. Fuzzy Sets Syst. 157(16), 2224–2240 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. H.H. Choi, LMI-based nonlinear fuzzy observer-controller design for uncertain MIMO nonlinear systems. IEEE Trans. Fuzzy Syst. 15(5), 956–971 (2007)

    Article  Google Scholar 

  7. M. Corless, J. Tu, State and input estimation for a class of uncertain systems. Automatica 34(6), 757–764 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  8. C. Edwards, X.G. Yan, S.K. Spurgeon, On the solvability of the constrained Lyapunov problem. IEEE Trans. Automat. Contr. 52(10), 1982–1987 (2007)

    Article  MathSciNet  Google Scholar 

  9. A. Fekih, H. Xu, F.N. Chowdhury, Neural networks based system identification techniques for model based fault detection of nonlinear systems. Int. J. Innov. Comput. Inf. Control 3(5), 1073–1085 (2007)

    Google Scholar 

  10. H. Gao, T. Chen, H ∞ estimation for uncertain systems with limited communication capacity. IEEE Trans. Automat. Contr. 52(11), 2070–2084 (2007)

    Article  MathSciNet  Google Scholar 

  11. H. Gao, T. Chen, Stabilization of nonlinear systems under variable sampling: A fuzzy control approach. IEEE Trans. Fuzzy Syst. 15(5), 972–983 (2007)

    Article  MathSciNet  Google Scholar 

  12. H. Gao, T. Chen, L. Wang, Robust fault detection with missing measurements. Int. J. Control 81(5), 804–819 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. L. Guo, F. Yang, J. Fang, Multiobjective filtering for nonlinear time-delay systems with nonzero initial conditions based on convex optimization. Circuits Syst. Signal Process. 25(5), 591–607 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  14. B. Jiang, M. Staroswiecki, V. Cocquempot, Fault identification for a class of time-delay systems, in Proceedings of the American Control Conference, Anchorage, AK (2002), pp. 2239–2244

  15. B. Jiang, M. Staroswiecki, V. Cocquempot, Fault accommodation for nonlinear dynamic systems. IEEE Trans. Automat. Contr. 51(9), 1578–1583 (2006)

    Article  MathSciNet  Google Scholar 

  16. N.P. Karampetakis, Computation of the generalized inverse of a polynomial matrix and applications. Linear Algebra Appl. 252(1–3), 35–60 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  17. J.H. Kim, C.H. Hyun, E. Kim, M. Park, Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model. IEEE Trans. Fuzzy Syst. 15(3), 359–369 (2007)

    Article  Google Scholar 

  18. K.R. Lee, J.H. Kim, E.T. Jeung, H.B. Park, Output feedback robust H ∞ control of uncertain fuzzy dynamic systems with time-varying delay. IEEE Trans. Fuzzy Syst. 8(6), 657–664 (2000)

    Article  Google Scholar 

  19. C.J. Lopez-Toribio, R.J. Patton, Takagi-Sugeno fuzzy fault-tolerant control for a non-linear system, in Proceedings of the 38th IEEE Conference on Decision and Control, Phoenix, AZ (1999), pp. 4368–4373

  20. X.J. Ma, Z.Q. Sun, Y.Y. He, Analysis and design of fuzzy controller and fuzzy observer. IEEE Trans. Fuzzy Syst. 6(1), 41–51 (1998)

    Article  Google Scholar 

  21. S.K. Nguang, P. Shi, H ∞ fuzzy output feedback control design for nonlinear systems: An LMI approach. IEEE Trans. Fuzzy Syst. 11(3), 331–340 (2003)

    Article  Google Scholar 

  22. S.K. Nguang, P. Shi, S.X. Ding, Delay-dependent fault estimation for uncertain time-delay nonlinear systems: An LMI approach. Int. J. Robust Nonlinear Control 16(18), 913–933 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  23. S.K. Nguang, P. Shi, S.X. Ding, Fault detection for uncertain fuzzy systems: An LMI approach. IEEE Trans. Fuzzy Syst. 15(6), 1251–1262 (2007)

    Article  Google Scholar 

  24. H. Noura, D. Theilliol, D. Sauter, Actuator fault-tolerant control design: Demonstration on a three-tank-system. Int. J. Syst. Sci. 31(9), 1143–1155 (2000)

    Article  MATH  Google Scholar 

  25. R.J. Patton, J. Chen, C.J. Lopez-Toribio, Fuzny observers for non-linear dynamic systems fault diagnosis, in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL (1998), pp. 84–89

  26. R. Penrose, A generalized inverse for matrices. Proc. Camb. Philos. Soc. 51, 406–413 (1955)

    Article  MathSciNet  MATH  Google Scholar 

  27. A.M. Pertew, H.J. Marquez, Q. Zhao, H ∞ observer design for Lipschitz nonlinear systems. IEEE Trans. Automat. Contr. 51(7), 1211–1216 (2006)

    Article  MathSciNet  Google Scholar 

  28. M.M. Polycarpou, Fault accommodation of a class of multivariable nonlinear dynamical systems using a learning approach. IEEE Trans. Automat. Contr. 46(5), 736–742 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Rajamani, Y.M. Cho, Existence and design of observers for nonlinear systems: Relation to distance to unobservability. Int. J. Control 69(5), 717–731 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  30. E.D. Sontag, The ISS philosophy as a unifying framework for stability-like behavior, in Nonlinear Control in the Year 2000 (Springer, Berlin, 2000), pp. 443–467

    Google Scholar 

  31. M. Staroswiecki, H. Yang, B. Jiang, Progressive accommodation of parametric faults in linear quadratic control. Automatica 43(12), 2070–2076 (2007)

    Article  MATH  Google Scholar 

  32. D. Theilliol, H. Noura, D. Sauter, Fault tolerant control method for actuator and component faults, in Proceedings of the 37th IEEE Conference on Decision and Control, Tampa, FL (1998), pp. 604–609

  33. S. Tong, Y. Li, Direct adaptive fuzzy backstepping control for a class of nonlinear systems. Int. J. Innov. Comput. Inf. Control 3(4), 887–896 (2007)

    Google Scholar 

  34. S. Tong, W. Wang, L. Qu, Decentralized robust control for uncertain T-S fuzzy large-scale systems with time-delay. Int. J. Innov. Comput. Inf. Control 3(3), 657–672 (2007)

    Google Scholar 

  35. K. Vijayaraghavan, R. Rajamani, J. Bokor, Quantitative fault estimation for a class of non-linear systems. Int. J. Control 80(1), 64–74 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. H. Wang, S. Daley, Actuator fault diagnosis: An adaptive observer-based technique. IEEE Trans. Automat. Contr. 41(7), 1073–1078 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  37. M. Wang, B. Chen, S. Tong, Adaptive fuzzy tracking control for strict-feedback nonlinear systems with unknown time delays. Int. J. Innov. Comput. Inf. Control 4(4), 829–837 (2008)

    Google Scholar 

  38. Z. Wang, D.P. Goodall, K.J. Burnham, On designing observers for time-delay systems with non-linear disturbances. Int. J. Control 75(11), 803–811 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  39. Y. Zhang, S.J. Qin, Adaptive actuator/component fault compensation for nonlinear systems. AIChE J. 54(9), 2404–2412 (2008)

    Article  Google Scholar 

  40. K. Zhang, B. Jiang, V. Cocquempot, Adaptive observer-based fast fault estimation. Int. J. Control Autom. Syst. 6(3), 320–326 (2008)

    Google Scholar 

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Authors and Affiliations

  1. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, P.R. China

    Ke Zhang & Bin Jiang

  2. Faculty of Advanced Technology, University of Glamorgan, Pontypridd, CF37 1DL, UK

    Peng Shi

  3. ILSCM, School of Science and Engineering, Victoria University, Melbourne, Australia

    Peng Shi

  4. School of Mathematics and Statistics, University of South Australia, Adelaide, Australia

    Peng Shi

Authors
  1. Ke Zhang
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  2. Bin Jiang
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  3. Peng Shi
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Corresponding author

Correspondence to Bin Jiang.

Additional information

This work is supported by the National Natural Science Foundation of China (90816023, 60811120024), Aeronautics Science Foundation of China (2007ZC52039), Natural Science Foundation of Jiangsu Province (BK2007195), Graduate Innovation Research Foundation of Jiangsu Province (CX08B_090Z), Doctoral Innovation Foundation of Nanjing University of Aeronautics and Astronautics (BCXJ08-03) and Engineering and Physical Sciences Research Council of UK (EP/F029195).

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Zhang, K., Jiang, B. & Shi, P. A New Approach to Observer-Based Fault-Tolerant Controller Design for Takagi-Sugeno Fuzzy Systems with State Delay. Circuits Syst Signal Process 28, 679–697 (2009). https://doi.org/10.1007/s00034-009-9109-4

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  • DOI: https://doi.org/10.1007/s00034-009-9109-4

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