In this study, the event-triggered distributed fault detection problem is investigated for a class of discrete-time uncertain systems in the finite frequency domain. A sensor network is utilised to collect the information of interest, and an event-triggered communication scheme is adopted to alleviate the communication burden. For the addressed problem, a distributed fault detection filter is designed based on the measurement information from its neighbouring nodes and itself by the given topology. In addition, a fashionable index, named as $H − / H ∞$ performance, is employed in order to simultaneously achieve the residual sensitivity to faults and the robustness against disturbances. By resorting to Euler's formula combined with Lyapunov stability theory, some sufficient conditions are established to satisfy the desired performance over a given finite-frequency domain, and the distributed fault detection filter gains are explicitly characterised by solving a series of linear matrix inequalities. A simulation example is conducted to illustrate the feasibility of the proposed filter design technique.

References

1. 1)
  - 10. Shi, C.-X., Yang, G.-H., Li, X.-J.: ‘Fault detection filter design with adaptive mechanism for linear uncertain polytopic systems in finite frequency domains’, IET Control Theory Appl., 2016, 10, (16), pp. 2027–2037.
2. 2)
  - 1. He, X., Wang, Z., Liu, Y., et al: ‘Fault-tolerant control for an internet-based three-tank system: accommodation to sensor bias faults’, IEEE Trans. Ind. Electron., 2017, 64, (3), pp. 2266–2275.
3. 3)
  - 30. Zhang, D., Shi, P., Wang, Q.-G., et al: ‘Distributed non-fragile filtering for T-S fuzzy systems with event-based communications’, Fuzzy Set. Syst., 2017, 306, pp. 137–152.
4. 4)
  - 35. Wang, L., Wang, Z., Wei, G., et al: ‘Observer-based consensus control for discrete-time multi-agent systems with coding-decoding communication protocol’, IEEE Trans. Cybern., DOI: 10.1109/TCYB.2018.2863664.
5. 5)
  - 8. Chadli, M., Davoodi, M., Meskin, N.: ‘Distributed state estimation, fault detection and isolation filter design for heterogeneous multi-agent linear parameter-varying systems’, IET Control Theory Appl., 2017, 11, (2), pp. 254–262.
6. 6)
  - 4. Shen, Q., 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, (2), pp. 274–285.
7. 7)
  - 32. Iwasakia, T., Harab, S., Fradkov, A.L.: ‘Time domain interpretations of frequency domain inequalities on (semi) finite ranges’, Syst. Control Lett., 2005, 54, pp. 681–691.
8. 8)
  - 33. Wang, Z., Yang, F., Ho, D.W.C., et al: ‘Robust H∞ filtering for stochastic time-delay systems with missing measurements’, IEEE Trans. Signal Process., 2006, 54, (7), pp. 2579–2587.
9. 9)
  - 9. Wang, J., Yang, G.-H., Liu, J.: ‘An LMI approach to H− index and mixed H−/H∞ fault detection observer design’, Automatica, 2007, 43, pp. 1656–1665.
10. 10)
  - 13. Gu, Y., Yang, G.-H.: ‘Fault detection for discrete-time Lipschitz non-linear systems in finite-frequency domain’, IET Control Theory Appl., 2017, 11, (14), pp. 2177–2186.
11. 11)
  - 39. Zhu, X., Xia, Y., Chai, S., et al: ‘Fault detection for vehicle active suspension systems in finite-frequency domain’, IET Control Theory Appl., 2019, 13, (3), pp. 387–394.
12. 12)
  - 12. Rambeaux, F., Hamelin, F., Sauter, D.: ‘Optimal thresholding for robust fault detection of uncertain systems’, Int. J. Robust Nonlinear Control, 2000, 10, pp. 1155–1173.
13. 13)
  - 27. Karimi, H.R., Niu, Y., Rossell, J.M., et al: ‘Analysis and synthesis of control systems over wireless digital channels’, J. Franklin Inst., 2017, 354, (9), pp. 3649–3653.
14. 14)
  - 24. Zhu, W., Jiang, Z.-P., Feng, G.: ‘Event-based consensus of multi-agent systems with general linear models’, Automatica, 2014, 50, (2), pp. 552–558.
15. 15)
  - 23. Smarsly, K., Law, K.: ‘Decentralized fault detection and isolation in wireless structural health monitoring systems using analytical redundancy’, Adv. Eng. Softw., 2014, 73, pp. 1–10.
16. 16)
  - 11. Hou, M., Patton, R.J.: ‘An LMI approach to H−/H∞ fault detection observers’. UKACC Int. Conf. on Control, Exeter, UK, 1996,vol. 96, pp. 305–310.
17. 17)
  - 38. Zhang, K., Jiang, B., Staroswiecki, M.: ‘Dynamic output feedback-fault tolerant controller design for takagi-sugeno fuzzy systems with actuator faults’, IEEE Trans. Fuzzy Syst., 2010, 18, (1), pp. 194–201.
18. 18)
  - 29. Wang, L., Wang, Z., Han, Q-L, et al: ‘Event-based variance-constrained H∞ filtering for stochastic parameter systems over sensor networks with successive missing measurements’, IEEE Trans. Cybern., 2018, 48, (3), pp. 1007–1017.
19. 19)
  - 37. Ding, D., Wang, Z., Han, Q.-L., et al: ‘Neural-network-based output-feedback control under round-robin scheduling protocols’, IEEE Trans. Cybern., 2019, 49, (6), pp. 2372–2384.
20. 20)
  - 16. Zhang, D., Xu, Z., Karimi, H.R., et al: ‘Distributed filtering for switched linear systems with sensor networks in presence of packet dropouts and quantization’, IEEE Trans. Circuits Syst. I, Reg. Pap., 2017, 64, (10), pp. 2783–2796.
21. 21)
  - 2. Li, J., Wu, C.-Y., Su, Q.: ‘Robust fault detection filter design for interconnected systems subject to packet dropouts and structure changes’, IET Control Theory Appl., 2018, 12, (3), pp. 368–376.
22. 22)
  - 22. Liu, K., Ma, Q., Gong, W., et al: ‘Self-diagnosis for detecting system failures in large-scale wireless sensor networks’, IEEE Trans. Wireless Commun., 2014, 13, (10), pp. 5535–5545.
23. 23)
  - 7. Zhong, M., Ding, S.X., Lam, J., et al: ‘An LMI approach to design robust fault detection filter for uncertain LTI systems’, Automatica, 2003, 39, (3), pp. 543–550.
24. 24)
  - 3. Long, Y., Yang, G.-H.: ‘Fault detection in finite frequency domain for networked control systems with missing measurements’, J. Franklin Inst., 2013, 9, (350), pp. 2605–2626.
25. 25)
  - 31. Chen, W., Ding, D., Ge, X., et al: ‘H∞ containment control of multi-agent systems under event-triggered communication scheduling: the finite-horizon case’, IEEE Trans. Cybern., to be published. DOI: 10.1109/TCYB.2018.2885567.
26. 26)
  - 36. Liu, S., Wang, Z., Wang, L., et al: ‘On quantized H∞ filtering for multi-rate systems under stochastic communication protocols: the finite-horizon case’, Inf. Sci., 2018, 459, pp. 211–223.
27. 27)
  - 18. Ding, D., Han, Q.-L., Wang, Z., et al: ‘A survey on model-based distributed control and filtering for industrial cyber-physical systems’, IEEE Trans. Ind. Inf., 2019, 15, (5), pp. 2483–2499.
28. 28)
  - 28. Hu, J., Wang, Z., Alsaadi, F.E., et al: ‘Event-based filtering for time-varying nonlinear systems subject to multiple missing measurements with uncertain missing probabilities’, Inf. Fusion, 2017, 38, pp. 74–83.
29. 29)
  - 19. Braca, P., Goldhahn, R., Ferri, G., et al: ‘Distributed information fusion in multistatic sensor networks for underwater surveillance’, IEEE Sens. J., 2016, 16, (11), pp. 4003–4014.
30. 30)
  - 17. Ding, D., Wang, Z., Dong, H., et al: ‘Distributed H∞ state estimation with stochastic parameters and nonlinearities through sensor networks: the finite-horizon case’, Automatica, 2012, 48, (8), pp. 1575–1585.
31. 31)
  - 5. Liu, J., Wang, J.L., Yang, G.-H.: ‘An LMI approach to minimum sensitivity analysis with application to fault detection’, Automatica, 2005, 11, (41), pp. 1995–2004.
32. 32)
  - 40. Tian, E., Wang, Z., Lei, Z., et al: ‘Probability-constrained filtering for a class of nonlinear systems with improved static event-triggered communication’, Int. J. Robust Nonlinear, 2019, 29, (5), pp. 1484–1498.
33. 33)
  - 14. Zhou, Z., Luan, L., Liu, F.: ‘Finite-frequency fault detection based on derandomisation for Markov jump linear system’, IET Control Theory Appl., 2018, 12, (8), pp. 1148–1155.
34. 34)
  - 21. Avci, O., Abdeljaber, O., Kiranyaz, S., et al: ‘Wireless and real-time structural damage detection: A novel decentralized method for wireless sensor networks’, J. Sound Vib., 2018, 424, pp. 158–172.
35. 35)
  - 34. Hu, J., Wang, Z., Gao, H., et al: ‘Robust sliding mode control for discrete stochastic systems with mixed time-delays, randomly occurring uncertainties and nonlinearities’, IEEE Trans. Ind. Electoron., 2012, 59, (7), pp. 3008–3015.
36. 36)
  - 25. Liu, J., Yue, D.: ‘Event-triggering in networked systems with probabilistic sensor and actuator faults’, Inf. Sci., 2013, 240, pp. 145–160.
37. 37)
  - 15. Iwasake, T., Hara, S.: ‘Generalized KYP lemma: unified frequency domain inequalities with design applications’, IEEE Trans. Autom. Control, 2005, 50, (1), pp. 41–59.
38. 38)
  - 6. Yang, Y., Ding, S.X., Li, L.: ‘Parameterization of nonlinear observer-based fault detection systems’, IEEE Trans. Autom. Control, 2016, 61, (11), pp. 3687–3692.
39. 39)
  - 20. Liu, S., Wang, Z., Wei, G., et al: ‘Distributed set-membership filtering for multirate systems under the Round-Robin scheduling over sensor networks’, IEEE Trans. Cybern., DOI: 10.1109/TCYB.2018.2885653.
40. 40)
  - 26. Donkers, M., Heemels, W.: ‘Output-based event-triggered control with guaranteed L∞ gain and improved and decentralised event-triggering’, IEEE Trans. Autom. Control, 2012, 57, (6), pp. 1326–1332.

Event-triggered distributed fault detection over sensor networks in finite-frequency domain

References

Related content