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Journal of Systems Science and Complexity

, Volume 31, Issue 6, pp 1405–1422 | Cite as

Sensor Fault Estimation and Fault-Tolerant Control for a Class of Takagi-Sugeno Markovian Jump Systems with Partially Unknown Transition Rates Based on the Reduced-Order Observer

  • Xiaohang Li
  • Dunke Lu
  • Wei Zhang
  • Fanglai Zhu
Article
  • 8 Downloads

Abstract

This paper addresses the problem on sensor fault estimation and fault-tolerant control for a class of Takagi-Sugeno Markovian jump systems, which are subjected to sensor faults and partially unknown transition rates. First, the original plant is extended to a descriptor system, where the original states and the sensor faults are assembled into the new state vector. Then, a novel reducedorder observer is designed for the extended system to simultaneously estimate the immeasurable states and sensor faults. Second, by using the estimated states obtained from the designed observer, a statefeedback fault-tolerant control strategy is developed to make the resulting closed-loop control system stochastically stable. Based on linear matrix inequality technique, algorithms are presented to compute the observer gains and control gains. The effectiveness of the proposed observer and controller are validated by a numerical example and a compared study, respectively, and the simulation results reveal that the proposed method can successfully estimate the sensor faults and guarantee the stochastic stability of the resulting closed-loop system.

Keywords

Fault-tolerant control Markovian jump system partially unknown transition rates reduced-order observer sensor fault estimation T-S fuzzy system 

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References

  1. [1]
    Xu Y, Lu R, Peng H, et al., Asynchronous dissipative state estimation for stochastic complex networks with quantized jumping coupling and uncertain measurements, IEEE Transactions on Neural Networks and Learning Systems, 2017, 28(2): 268–277.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Lu R, Wu F, and Xue A, Networked control with reset quantized state based on bernoulli processing, IEEE Transactions on Industrial Electronics, 2014, 61(9): 4838–4846.CrossRefGoogle Scholar
  3. [3]
    Fei Z, Guan C, and Shi P, Further results on H∞ control for discrete-time Markovian jump time-delay systems, International Journal of Control, 2017, 90(7): 1505–1517.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Xu Y, Lu R, Shi P, et al., Robust estimation for neural networks with randomly occurring distributed delays and Markovian jump coupling, IEEE Transactions on Neural Networks and Learning Systems, 2017, 29(4): 845–855.MathSciNetCrossRefGoogle Scholar
  5. [5]
    Xu Y, Wang Z, Yao D, et al., State estimation for periodic neural networks with uncertain weight matrices and Markovian jump channel states, IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2017, DOI: 10.1109/TSMC.2017.2708700.Google Scholar
  6. [6]
    Li H, Shi P, Yao D, et al., Observer-based adaptive sliding mode control for nonlinear Markovian jump systems, Automatica, 2016, 64: 133–142.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    Kwon N K, Park I S, and Park P G, H∞ control for singular Markovian jump systems with incomplete knowledge of transition probabilities, Applied Mathematics and Computation, 2017, 295: 126–135.MathSciNetCrossRefGoogle Scholar
  8. [8]
    Zhang L and Boukas E K, Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities, Automatica, 2009, 45(2): 463–468.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    Zhang L and Boukas E K, control for discrete-time Markovian jump linear systems with partly unknown transition probabilities, International Journal of Robust and Nonlinear Control, 2009, 19(8): 868–883.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [10]
    Liu M, Shi P, Zhang L, et al., Fault-tolerant control for nonlinear Markovian jump systems via proportional and derivative sliding mode observer technique, IEEE Transactions on Circuits and Systems I: Regular Papers, 2011, 58(11): 2755–2764.MathSciNetCrossRefGoogle Scholar
  11. [11]
    Li H, Gao H, Shi P, et al., Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach, Automatica, 2014, 50(7): 1825–1834.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    Shi P, Liu M, and Zhang L, Fault-tolerant sliding-mode-observer synthesis of Markovian jump systems using quantized measurements, IEEE Transactions on Industrial Electronics, 2015, 62(9): 5910–5918.CrossRefGoogle Scholar
  13. [13]
    Li X H and Zhu F L, Fault-tolerant control for Markovian jump systems with general uncertain transition rates against simultaneous actuator and sensor faults, International Journal of Robust and Nonlinear Control, 2017, 27(18): 4245–4274.MathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    Yin S, Yang H, and Kaynak O, Sliding mode observer-based FTC for Markovian jump systems with actuator and sensor faults, IEEE Transactions on Automatic Control, 2017, 62(7): 3551–3558.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    Lu D, Zeng G, and Liu J, Non-fragile simultaneous actuator and sensor fault-tolerant control design for Markovian jump systems based on adaptive observer: Fault-tolerant control design for Markovian jump systems, Asian Journal of Control, 2017, DOI: 10.1002/asjc.1534.Google Scholar
  16. [16]
    Lu D, Li X, Liu J, et al., Fault estimation and fault-tolerant control of Markovian jump system with mixed mode-dependent time-varying delays via the adaptive observer approach, Journal of Dynamic Systems, Measurement, and Control, 2017, 139(3): 031002.Google Scholar
  17. [17]
    Ren W, Wang C, and Lu Y, Fault estimation for time-varying Markovian jump systems with randomly occurring nonlinearities and time delays, Journal of the Franklin Institute, 2017, 354(3): 1388–1402.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    Chen L, Huang X, and Fu S, Fault-tolerant control for Markovian jump delay systems with an adaptive observer approach, Circuits, Systems, and Signal Processing, 2016, 35(12): 4290–4306.zbMATHGoogle Scholar
  19. [19]
    He S P, Fault estimation for TS fuzzy Markovian jumping systems based on the adaptive observer, International Journal of Control, Automation and Systems, 2014, 12(5): 977–985.CrossRefGoogle Scholar
  20. [20]
    Zhang J, Swain A K, and Nguang S K, Robust sensor fault estimation and fault-tolerant control for uncertain Lipschitz nonlinear systems, American Control Conference (ACC), IEEE, 2014, 5515–5520.Google Scholar
  21. [21]
    Liu M, Cao X, and Shi P, Fault estimation and tolerant control for fuzzy stochastic systems, IEEE Transactions on Fuzzy Systems, 2013, 21(2): 221–229.CrossRefGoogle Scholar
  22. [22]
    Zhang J, Swain A K, and Nguang S K, Robust sensor fault estimation scheme for satellite attitude control systems, Journal of the Franklin Institute, 2013, 350(9): 2581–2604.MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    Du D, Jiang B, and Shi P, Sensor fault estimation and accommodation for discrete-time switched linear systems, IET Control Theory & Applications, 2014, 8(11): 960–967.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Ichalal D, Marx B, Ragot J, et al., Sensor fault tolerant control of nonlinear Takagi-Sugeno systems, Application to vehicle lateral dynamics, International Journal of Robust and Nonlinear Control, 2016, 26(7): 1376–1394.MathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    Lpez-Estrada F R, Ponsart J C, Astorga-Zaragoza C M, et al., Robust sensor fault estimation for descriptorClpv systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor, International Journal of Applied Mathematics and Computer Science, 2015, 25(2): 233–244.MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    Aouaouda S, Chadli M, and Boukhnifer M, Speed sensor fault tolerant controller design for induction motor drive in EV, Neurocomputing, 2016, 214: 32–43.CrossRefGoogle Scholar
  27. [27]
    Li X, Lu D, Zeng G, et al., Integrated fault estimation and non-fragile fault tolerant control design for uncertain Takagi-Sugeno fuzzy systems with actuator fault and sensor fault, IET Control Theory & Applications, 2017, 11(10): 1542–1553.MathSciNetCrossRefGoogle Scholar
  28. [28]
    Li X, Zhu F, Chakrabarty A, et al., Non-fragile fault-tolerant fuzzy observer-based controller design for nonlinear systems, IEEE Transactions on Fuzzy Systems, 2016, 24(6): 1679–1689.CrossRefGoogle Scholar
  29. [29]
    Li Y X and Yang G H, Fuzzy adaptive output feedback fault-tolerant tracking control of a class of uncertain nonlinear systems with nonaffine nonlinear faults, IEEE Transactions on Fuzzy Systems, 2016, 24(1): 223–234.CrossRefGoogle Scholar
  30. [30]
    Lan J and Patton R J, Integrated design of fault-tolerant control for nonlinear systems based on fault estimation and TS fuzzy modelling, IEEE Transactions on Fuzzy Systems, 2017, 25(5): 1141–1154.CrossRefGoogle Scholar

Copyright information

© Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xiaohang Li
    • 1
    • 2
  • Dunke Lu
    • 1
  • Wei Zhang
    • 3
  • Fanglai Zhu
    • 4
  1. 1.School of Electronic and Electric EngineeringShanghai University of Engineering ScienceShanghaiChina
  2. 2.School of Electrical Engineering and AutomationHenan Polytechnic UniversityJiaozuoChina
  3. 3.Engineering Training CenterShanghai University of Engineering ScienceShanghaiChina
  4. 4.College of Electronics and Information EngineeringTongji UniversityShanghaiChina

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