Asymptotic state estimation for linear systems with sensor and actuator faults


This paper investigates the asymptotic state estimation problem for linear systems with sensor and actuator faults, where the faults are modeled via multiple modes. For the case of sensor faults, we first introduce a new notion of detectability, i.e., detectability of system against sensor faults. The notion helps to address the question of whether it is possible to asymptotically estimate the system state by using the control input and system output, irrespective of which mode the system is in and what values the fault signals are. A necessary and sufficient condition for the system to be detectable against sensor faults is given, and then two switched observers are proposed for asymptotic state estimation with the help of maximin strategy. For the system with fault modes, we provide the explicit form of the switched observer, which is based on a bank of \(\frac{\ell(\ell+1)}{2}\) Luenberger-like or sliding-mode observers. Furthermore, extensions to the case of sensor and actuator faults are further studied. Finally, a simulation example of a reduced-order aircraft system is provided to show the effectiveness of the proposed approaches.

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  1. 1

    Luenberger D. Observers for multivariable systems. IEEE Trans Autom Control, 1966, 11: 190–197

    Article  Google Scholar 

  2. 2

    Zhou D H, Qin L G, He X, et al. Distributed sensor fault diagnosis for a formation system with unknown constant time delays. Sci China Inf Sci, 2018, 61: 112205

    Article  Google Scholar 

  3. 3

    Kudva P, Viswanadham N, Ramakrishna A. Observers for linear systems with unknown inputs. IEEE Trans Autom Control, 1980, 25: 113–115

    MathSciNet  Article  Google Scholar 

  4. 4

    Kalsi K, Lian J M, Hui S, et al. Sliding-mode observers for systems with unknown inputs: a high-gain approach. Automatica, 2010, 46: 347–353

    MathSciNet  Article  Google Scholar 

  5. 5

    de Souza C E, Coutinho D, Kinnaert M. Mean square state estimation for sensor networks. Automatica, 2016, 72: 108–114

    MathSciNet  Article  Google Scholar 

  6. 6

    Zheng G, Bejarano F J. Observer design for linear singular time-delay systems. Automatica, 2017, 80: 1–9

    MathSciNet  Article  Google Scholar 

  7. 7

    Shi D W, Chen T W, Darouach M. Event-based state estimation of linear dynamic systems with unknown exogenous inputs. Automatica, 2016, 69: 275–288

    MathSciNet  Article  Google Scholar 

  8. 8

    Park G, Shim H. Guaranteeing almost fault-free tracking performance from transient to steady-state: a disturbance observer approach. Sci China Inf Sci, 2018, 61: 070224

    MathSciNet  Article  Google Scholar 

  9. 9

    Chong M S, Wakaiki M, Hespanha J P. Observability of linear systems under adversarial attacks. In: Processings of American Control Conference, 2015. 2439–2444

  10. 10

    Edwards C, Spurgeon S K, Patton R J. Sliding mode observers for fault detection and isolation. Automatica, 2000, 36: 541–553

    MathSciNet  Article  Google Scholar 

  11. 11

    Edwards C, Tan C P. Sensor fault tolerant control using sliding mode observers. Control Eng Pract, 2006, 14: 897–908

    Article  Google Scholar 

  12. 12

    Park T G. Estimation strategies for fault isolation of linear systems with disturbances. IET Control Theory Appl, 2010, 4: 2781–2792

    MathSciNet  Article  Google Scholar 

  13. 13

    Alwi H, Edwards C, Tan C P. Sliding mode estimation schemes for incipient sensor faults. Automatica, 2009, 45: 1679–1685

    MathSciNet  Article  Google Scholar 

  14. 14

    Rafaralahy H, Richard E, Boutayeb M, et al. Sensor diagnosis and state estimation for a class of skew symmetric time-varying systems. Automatica, 2012, 48: 2284–2289

    MathSciNet  Article  Google Scholar 

  15. 15

    Lan J, Patton R J. A new strategy for integration of fault estimation within fault-tolerant control. Automatica, 2016, 69: 48–59

    MathSciNet  Article  Google Scholar 

  16. 16

    Wang X, Tan C P, Zhou D. A novel sliding mode observer for state and fault estimation in systems not satisfying matching and minimum phase conditions. Automatica, 2017, 79: 290–295

    MathSciNet  Article  Google Scholar 

  17. 17

    Gao Z, Ding S X. Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems. Automatica, 2007, 43: 912–920

    MathSciNet  Article  Google Scholar 

  18. 18

    Yang G H, Wang H. Fault detection for a class of uncertain state-feedback control systems. IEEE Trans Control Syst Technol, 2010, 18: 201–212

    Article  Google Scholar 

  19. 19

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

    Article  Google Scholar 

  20. 20

    Li X J, Yang G H. Fault detection in finite frequency domain for Takagi-Sugeno fuzzy systems with sensor faults. IEEE Trans Cybern, 2014, 44: 1446–1458

    Article  Google Scholar 

  21. 21

    Yang G H, Ye D. Reliable H control of linear systems with adaptive mechanism. IEEE Trans Autom Control, 2010, 55: 242–247

    MathSciNet  Article  Google Scholar 

  22. 22

    Jiang B, Yang H, Shi P. Switching fault tolerant control design via global dissipativity. Int J Syst Sci, 2010, 41: 1003–1012

    MathSciNet  Article  Google Scholar 

  23. 23

    Tong S C, Huo B Y, Li Y M. Observer-based adaptive decentralized fuzzy fault-tolerant control of nonlinear large-scale systems with actuator failures. IEEE Trans Fuzzy Syst, 2014, 22: 1–15

    Article  Google Scholar 

  24. 24

    Liu M, Ho D W C, Shi P. Adaptive fault-tolerant compensation control for Markovian jump systems with mismatched external disturbance. Automatica, 2015, 58: 5–14

    MathSciNet  Article  Google Scholar 

  25. 25

    Li Y X, Yang G H. Adaptive asymptotic tracking control of uncertain nonlinear systems with input quantization and actuator faults. Automatica, 2016, 72: 177–185

    MathSciNet  Article  Google Scholar 

  26. 26

    Deng C, Yang G H. Distributed adaptive fault-tolerant control approach to cooperative output regulation for linear multi-agent systems. Automatica, 2019, 103: 62–68

    MathSciNet  Article  Google Scholar 

  27. 27

    Hautus M L J. Strong detectability and observers. Linear Algebra Appl, 1983, 50: 353–368

    MathSciNet  Article  Google Scholar 

  28. 28

    Zhang W, Zhang H, Chen B S. Generalized Lyapunov equation approach to state-dependent stochastic stabilization/detectability criterion. IEEE Trans Autom Control, 2008, 53: 1630–1642

    MathSciNet  Article  Google Scholar 

  29. 29

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

    MathSciNet  Article  Google Scholar 

  30. 30

    Filippov A F. Differential Equations with Discontinuous Right-Hand Sides. Dordrecht: KluwerAcademic Publishers, 1988

    Google Scholar 

  31. 31

    Slotine J J E, Li W. Applied Nonlinear Control. Englewood Cliffs: Prentice-Hall, 1991

    Google Scholar 

  32. 32

    Siwakosit W, Hess R A. Multi-input/multi-output reconfigurable flight control design. J Guid Control Dyn, 2001, 24: 1079–1088

    Article  Google Scholar 

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This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61733005, 61673172, 61663013, 61803155, 51565012) and Science and Technology Research Project of Jiangxi Education Department (Grant No. 170376).

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Correspondence to Hui Yang.

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Xie, CH., Yang, H., Wang, D. et al. Asymptotic state estimation for linear systems with sensor and actuator faults. Sci. China Inf. Sci. 62, 212202 (2019).

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  • asymptotic state estimation
  • observer
  • linear systems
  • sensor faults
  • actuator faults