Fault detection for a class of non-linear networked control systems in the presence of Markov sensors assignment with partially known transition probabilities

Yanqian Wang; Junwei Lu; Ze Li; Yuming Chu

Fault detection for a class of non-linear networked control systems in the presence of Markov sensors assignment with partially known transition probabilities

View Fulltext

Author(s): Yanqian Wang ^{1, 2} ; Junwei Lu ³ ; Ze Li ⁴ ; Yuming Chu ⁵
- Affiliations: 1: School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, People's Republic of China;
  2: School of Information and Electronic Engineering, Shandong Institute of Business and Technology, Yantai, Shandong 264005, People's Republic of China;
  3: School of Electrical and Automation Engineering, Nanjing Normal University, 78 Bancang Street, Nanjing, Jiangsu 210042, People's Republic of China;
  4: School of Mechanical and Electrical Engineering, Suzhou University of Science and Technology, Suzhou, Jiangsu 215000, People's Republic of China;
  5: School of Science, Huzhou Teachers College, Huzhou, Zhejiang 313000, People's Republic of China
Source: Volume 9, Issue 10, 25 June 2015, p. 1491 – 1500
DOI: 10.1049/iet-cta.2013.0802 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 05/09/2013, Accepted 16/11/2014, Revised 20/10/2014, Published 11/05/2015

In this study, the problem of fault detection for a class of discrete-time non-linear networked control systems is investigated. An event modelled as a Markov chain taking matrix values in a certain set with partially known transition probabilities is utilised to characterise the phenomenon of the sensors assignment. A full-order mode-dependent fault detection filter is constructed and the corresponding fault detection problem is converted into an H _∞ filtering problem of a Markov jump system with partially known transition probabilities. Sufficient conditions for the existence of the fault detection filter are formulated as a linear matrix inequality-based convex optimisation problem. If the convex optimisation problem has a feasible solution, the corresponding fault detection filter parameters are determined. A numerical example with four cases of transition probability matrices is presented to show the usefulness of the developed method.

References

1. 1)
  - P. Zhang , S. Ding , G. Wang , D. Zhou . Fault detection of linear discrete-time periodic systems. IEEE Trans. Autom. Control , 2 , 239 - 244
2. 2)
  - D. Hristu-Varsakelis . Short-period communication and the role of zero-order holding in networked control systems. IEEE Trans. Autom. Control , 1285 - 1290
3. 3)
  - X. He , Z. Wang , D. Zhou . Robust fault detection for networked systems with communication delay and data missing. Automatica , 11 , 2634 - 2639
4. 4)
  - 12. Tian, E.G., Zhao, X.: ‘Robust H∞ control for uncertain networked systems with communication constraints’, J. Franklin Inst., 2013, 350, (7), pp. 1926–1943 (doi: 10.1016/j.jfranklin.2013.02.010).
5. 5)
  - 13. Lu, Z.B., Guo, G.: ‘Control with sensors/actuators assigned by Markov chains: transition rates partially unknown’, IET Control Theory Appl., 2013, 7, (8), pp. 1088–1097 (doi: 10.1049/iet-cta.2012.0879).
6. 6)
  - L.E. Ghaoui , F. Oustry , M. AitRami . A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Autom. Control , 8 , 1171 - 1176
7. 7)
  - 23. Long, Y., Yang, G.H.: ‘Fault detection for networked control systems subject to quantisation and packet dropout’, Int. J. Syst. Sci., 2013, 44, (6), pp. 1150–1159 (doi: 10.1080/00207721.2012.658882).
8. 8)
  - G. Guo . Linear systems with medium access constraint and Markov actuator assignment. IEEE Trans. Circuits Syst. I , 11 , 2999 - 3010
9. 9)
  - Y. Wang , H. Ye , S.X. Ding , G. Wang , D. Zhou . Residual generation and evaluation of networked control systems subject to random packet dropout. Automatica , 2427 - 2434
10. 10)
  - 24. Jiang, S., Fang, H.J.: ‘Robust fault detection for networked control systems with nonlinear disturbances and imperfect measurements’, Int. J. Syst. Sci., 2013, 44, (11), pp. 2027–2038 (doi: 10.1080/00207721.2012.683833).
11. 11)
  - R.A. Gupta , M.Y. Chow . Networked control system: overview and research trends. IEEE Trans. Ind. Electron. , 7 , 2527 - 2535
12. 12)
  - 16. Feng, J., Wang, S.Q., Zhao, Q.: ‘Closed-loop design of fault detection for networked non-linear systems with mixed delays and packet losses’, IET Control Theory Appl., 2013, 7, (6), pp. 858–868 (doi: 10.1049/iet-cta.2012.0987).
13. 13)
  - 9. Liu, T., Zhang, H., Chen, Q.J., et al: ‘H∞control for networked control systems with limited information’, J. Franklin Inst., 2012, 349, (5), pp. 1915–1929 (doi: 10.1016/j.jfranklin.2012.02.017).
14. 14)
  - S. Kim , I. Hwang , C.E. Seah . A survey of fault detection, isolation, and reconfiguration methods. IEEE Trans. Control Syst. Technol. , 3 , 636 - 653
15. 15)
  - 7. Hristu-Varsakelis, D., Zhang, L.: ‘LQG control of networked control systems with access constraints and delays’, Int. J. Control, 2008, 81, (8), pp. 1266–1280 (doi: 10.1080/00207170701697742).
16. 16)
  - 8. Long, Y., Yang, G.-H.: ‘Fault detection for a class of networked control systems with finite-frequency servo inputs and random packet dropouts’, IET Control Theory Appl., 2012, 6, (15), 2397–2408 (doi: 10.1049/iet-cta.2012.0333).
17. 17)
  - L. Zhang , D. Hristu-Varsakelis . Communication and control co-design for networked control systems. Automatica , 953 - 958
18. 18)
  - J. Hespanha , P. Naghshtabrizi , Y. Xu . A survey of recent results in networked control systems. Proc. IEEE , 1 , 138 - 162
19. 19)
  - 30. Hu, S., Yue, D., Liu, J.: ‘H∞ filtering for networked systems with partly known distribution transmission delays’, Inf. Sci., 2012, 194, pp. 270–282 (doi: 10.1016/j.ins.2011.12.026).
20. 20)
  - 25. Wan, X.B., Fang, H.J.: ‘Fault detection for discrete-time networked nonlinear systems with incomplete measurements’, Int. J. Syst. Sci., 2013, 44, (11), pp. 2068–2081 (doi: 10.1080/00207721.2012.684899).
21. 21)
  - 18. Peng, C., Yang, T.C.: ‘Event-triggered communication and H∞ control co-design for networked control systems’, Automatica, 2013, 49, (5), pp. 1326–1332 (doi: 10.1016/j.automatica.2013.01.038).
22. 22)
  - 5. Branicky, M.S., Phillips, S.M., Zhang, W.: ‘Scheduling and feedback co-design for networked control systems’. Proc. of the 41st IEEE Conf. on Decision and Control, Las Vegas, Nevada USA, December 2002, (2), pp. 1211–1217.
23. 23)
  - G.C. Walsh , H. Ye , L.G. Bushnell . Stability analysis of networked control systems. IEEE Trans. Control Syst. Technol. , 438 - 446
24. 24)
  - 26. Guo, G., Lu, Z., Shi, P.: ‘Event-driven actuators: to zero or to hold’?Int. J. Robust Nonlinear Control, 2013, DOI: 10.1002/rnc.3023.
25. 25)
  - G. Guo , Z. Lu , Q.L. Han . Control with Markov sensors/actuators assignment. IEEE Trans. Autom. Control , 7 , 1799 - 1804
26. 26)
  - W. Zhang , M.S. Branicky , S.M. Phillips . Stability of networked control systems. IEEE Control Syst. Mag. , 84 - 99
27. 27)
  - 10. Guo, G., Lu, Z.B.: ‘Markov actuator assignment for networked control systems’, Eur. J. Control, 2012, 18, (4), pp. 323–330 (doi: 10.3166/ejc.18.323-330).
28. 28)
  - 31. Zhang, Y., Liu, Z., Fang, H., et al: ‘ℋ∞ fault detection for nonlinear networked systems with multiple channels data transmission pattern’, Inf. Sci., 2013, 221, pp. 534–543 (doi: 10.1016/j.ins.2012.09.026).
29. 29)
  - 21. Liu, B., Xian, Y.Q., Yang, Y., Fu, M.Y.: ‘Robust fault detection of linear systems over networks with bounded packet loss’, J. Franklin Inst., 2012, 349, (7), pp. 2480–2499 (doi: 10.1016/j.jfranklin.2012.05.011).

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

Fault detection for a class of non-linear networked control systems in the presence of Markov sensors assignment with partially known transition probabilities

References

Related content