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Fault detection and isolation for linear parameter-varying systems with time-delays: a geometric approach

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Abstract

Fault detection and isolation (FDI) problems for linear parameter-varying (LPV) systems with state time-delays are studied in this paper. By defining the concept of unobservability subspace and designing its calculation algorithm, the geometric approach is introduced to the time-delay LPV systems. Utilizing Wirtinger-based integral inequality, we obtain a sufficient condition to solve the so-called H∞-based residual generation problem for the LPV systems. In this paper, we consider two cases: the time delay is known and the time delay is unknown but its estimated value can be obtained. Corresponding observers are proposed for both cases based on the geometric approach and H∞ techniques. Lyapunov-Krasovskii functional is utilized to handle the time-delays and Wirtinger’s inequality is employed to reduce conservatism. Numerical examples are presented to demonstrate the effectiveness of the proposed approach.

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References

  1. Straka O, Punčochář I. Distributed design for active fault diagnosis. Int J Syst Sci, 2022, 53: 562–574

    Article  MathSciNet  MATH  Google Scholar 

  2. Huang D R, Hua X X, Mi B, et al. Incipient fault diagnosis on active disturbance rejection control. Sci China Inf Sci, 2022, 65: 199202

    Article  MathSciNet  Google Scholar 

  3. He X, Guo Y Q, Zhang Z, et al. Active fault diagnosis for dynamic systems. Acta Autom Sin, 2020, 46: 1557–1570

    Google Scholar 

  4. Hu J, Wang Z D, Liu G P. Delay compensation-based state estimation for time-varying complex networks with incomplete observations and dynamical bias. IEEE Trans Cybern, 2022, 52: 12071–12083

    Article  Google Scholar 

  5. Pang Z H, Xia C G, Zhai W F, et al. Networked active fault-tolerant predictive control for systems with random communication constraints and actuator/sensor faults. IEEE Trans Circuits Syst II, 2022, 69: 2166–2170

    Google Scholar 

  6. Zou L, Wang Z D, Hu J, et al. Communication-protocol-based analysis and synthesis of networked systems: progress, prospects and challenges. Int J Syst Sci, 2021, 52: 3013–3034

    Article  MathSciNet  MATH  Google Scholar 

  7. Zhang Z, He X. Active fault diagnosis for linear systems: within a signal processing framework. IEEE Trans Instrum Meas, 2022, 71: 3505009

    Google Scholar 

  8. Qin L G, He X, Yan R Y, et al. Active fault-tolerant control for a quadrotor with sensor faults. J Intell Robot Syst, 2017, 88: 449–467

    Article  Google Scholar 

  9. Wang Y A, Shen B, Zou L. Recursive fault estimation with energy harvesting sensors and uniform quantization effects. IEEE CAA J Autom Sin, 2022, 9: 926–929

    Article  Google Scholar 

  10. Bu X Y, Dong H L, Wang Z D, et al. Non-fragile distributed fault estimation for a class of nonlinear time-varying systems over sensor networks: the finite-horizon case. IEEE Trans Signal Inf Process over Networks, 2019, 5: 61–69

    Article  MathSciNet  Google Scholar 

  11. Cao F F, Zhang Z, He X. Active fault isolation of over-actuated systems based on a control allocation approach. IEEE Trans Instrum Meas, 2022, 71: 3513410

    Google Scholar 

  12. Cai M, He X, Zhou D H. Performance-improved finite-time fault-tolerant control for linear uncertain systems with intermittent faults: an overshoot suppression strategy. Int J Syst Sci, 2022, 53: 3408–3425

    Article  MathSciNet  Google Scholar 

  13. Gao C, Wang Z D, He X, et al. Fault-tolerant consensus control for multiagent systems: an encryption-decryption scheme. IEEE Trans Automat Contr, 2022, 67: 2560–2567

    Article  MathSciNet  MATH  Google Scholar 

  14. Xue T, Ding S X, Zhong M, et al. An integrated design scheme for SKR-based data-driven dynamic fault detection systems. IEEE Trans Ind Inf, 2022, 18: 6828–6839

    Article  Google Scholar 

  15. Zhang J F, Zhang Q H, He X, et al. Compound-fault diagnosis of rotating machinery: a fused imbalance learning method. IEEE Trans Contr Syst Technol, 2020, 29: 1462–1474

    Article  Google Scholar 

  16. Mukaidani H, Xu H. Robust SOF Stackelberg game for stochastic LPV systems. Sci China Inf Sci, 2021, 64: 200202

    Article  MathSciNet  Google Scholar 

  17. Weiss Y, Allerhand L I, Arogeti S. Yaw stability control for a rear double-driven electric vehicle using LPV-H∞ methods. Sci China Inf Sci, 2018, 61: 070206

    Article  MathSciNet  Google Scholar 

  18. Duan G R. Fully actuated system approaches for continuous-time delay systems: part 1. Systems with state delays only. Sci China Inf Sci, 2023, 66: 112201

    Article  MathSciNet  Google Scholar 

  19. Liu W Y, Bai Y J, Jiao L, et al. Safety guarantee for time-delay systems with disturbances. Sci China Inf Sci, 2023, 66: 132102

    Article  MathSciNet  Google Scholar 

  20. Hou T, Liu Y Y, Deng F Q. Stability for discrete-time uncertain systems with infinite Markov jump and time-delay. Sci China Inf Sci, 2021, 64: 152202

    Article  MathSciNet  Google Scholar 

  21. Han Y T, Xu Z, Guo H. Robust predictive control of a supercavitating vehicle based on time-delay characteristics and parameter uncertainty. Ocean Eng, 2021, 237: 109627

    Article  Google Scholar 

  22. Tasoujian S, Salavati S, Franchek M A, et al. Robust delay-dependent LPV synthesis for blood pressure control with real-time Bayesian parameter estimation. IET Control Theor Appl, 2020, 14: 1334–1345

    Article  MathSciNet  Google Scholar 

  23. Zhang X P, Tsiotras P, Knospe C. Stability analysis of LPV time-delayed systems. Int J Control, 2002, 75: 538–558

    Article  MathSciNet  MATH  Google Scholar 

  24. Hassanabadi A H, Shafiee M, Puig V. Actuator fault diagnosis of singular delayed LPV systems with inexact measured parameters via PI unknown input observer. IET Control Theor Appl, 2017, 11: 1894–1903

    Article  MathSciNet  Google Scholar 

  25. Hamdi H, Rodrigues M, Mechmeche C, et al. Observer-based fault diagnosis for time-delay LPV descriptor systems. IFAC-PapersOnLine, 2018, 51: 1179–1184

    Article  Google Scholar 

  26. Xu F, Tan J B, Wang X Q, et al. Generalized set-theoretic unknown input observer for LPV systems with application to state estimation and robust fault detection. Int J Robust Nonlinear Control, 2017, 27: 3812–3832

    MathSciNet  MATH  Google Scholar 

  27. Massoumnia M A. A geometric approach to the synthesis of failure detection filters. IEEE Trans Automat Contr, 1986, 31: 839–846

    Article  MathSciNet  MATH  Google Scholar 

  28. Massoumnia M A, Verghese G C, Willsky A S. Failure detection and identification. IEEE Trans Automat Contr, 1989, 34: 316–321

    Article  MathSciNet  MATH  Google Scholar 

  29. Bokor J, Balas G. Detection filter design for LPV systems—a geometric approach. Automatica, 2004, 40: 511–518

    Article  MathSciNet  MATH  Google Scholar 

  30. Balas G, Bokor J, Szabo Z. Invariant subspaces for LPV systems and their applications. IEEE Trans Automat Contr, 2003, 48: 2065–2069

    Article  MathSciNet  MATH  Google Scholar 

  31. Basile G, Marro G. Controlled and Conditioned Invariants in Linear System Theory. Englewood Cliffs: Prentice Hall, 1992

    MATH  Google Scholar 

  32. Meskin N, Khorasani K. Robust fault detection and isolation of time-delay systems using a geometric approach. Automatica, 2009, 45: 1567–1573

    Article  MathSciNet  MATH  Google Scholar 

  33. Meskin N, Khorasani K. Fault detection and isolation of distributed time-delay systems. IEEE Trans Automat Contr, 2009, 54: 2680–2685

    Article  MathSciNet  MATH  Google Scholar 

  34. Meskin N, Khorasani K. A geometric approach to fault detection and isolation of continuous-time Markovian jump linear systems. IEEE Trans Automat Contr, 2010, 55: 1343–1357

    Article  MathSciNet  MATH  Google Scholar 

  35. Seuret A, Gouaisbaut F. Wirtinger-based integral inequality: application to time-delay systems. Automatica, 2013, 49: 2860–2866

    Article  MathSciNet  MATH  Google Scholar 

  36. Park P G, Ko J W, Jeong C. Reciprocally convex approach to stability of systems with time-varying delays. Automatica, 2011, 47: 235–238

    Article  MathSciNet  MATH  Google Scholar 

  37. Yang X Q, Yin S, Kaynak O. Robust identification of LPV time-delay system with randomly missing measurements. IEEE Trans Syst Man Cybern Syst, 2018, 48: 2198–2208

    Article  Google Scholar 

  38. Yang X Q, Huang B, Gao H J. A direct maximum likelihood optimization approach to identification of LPV time-delay systems. J Franklin Institute, 2016, 353: 1862–1881

    Article  MathSciNet  MATH  Google Scholar 

  39. Bayrak A, Tatlicioglu E. A novel online adaptive time delay identification technique. Int J Syst Sci, 2016, 47: 1574–1585

    Article  MathSciNet  MATH  Google Scholar 

  40. Ren X M, Rad A B. Identification of nonlinear systems with unknown time delay based on time-delay neural networks. IEEE Trans Neural Netw, 2007, 18: 1536–1541

    Article  Google Scholar 

  41. Wu F, Grigoriadis K M. LPV systems with parameter-varying time delays: analysis and control. Automatica, 2001, 37: 221–229

    Article  MathSciNet  MATH  Google Scholar 

  42. Briat C, Sename O, Lafay J F. Memory-resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays. Syst Control Lett, 2010, 59: 451–459

    Article  MathSciNet  MATH  Google Scholar 

  43. Hu Y M, Duan G. H∞ finite-time control for LPV systems with parameter-varying time delays and external disturbance via observer-based state feedback. J Franklin Institute, 2019, 356: 6303–6327

    Article  MathSciNet  MATH  Google Scholar 

  44. Zope R, Mohammadpour J, Grigoriadis K, et al. Delay-dependent H∞ control for LPV systems with fast-varying time delays. In: Proceedings of the 2012 American Control Conference, Montreal, 2012. 775–780

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61733009), National Key Research and Development Program of China (Grant No. 2022YFB25031103), and Huaneng Group Science and Technology Research Project.

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Authors and Affiliations

  1. Department of Automation, Tsinghua University, Beijing, 100084, China

    Zhao Zhang & Xiao He

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  1. Zhao Zhang
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  2. Xiao He
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Correspondence to Xiao He.

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Zhang, Z., He, X. Fault detection and isolation for linear parameter-varying systems with time-delays: a geometric approach. Sci. China Inf. Sci. 66, 172202 (2023). https://doi.org/10.1007/s11432-022-3632-2

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  • DOI: https://doi.org/10.1007/s11432-022-3632-2

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