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Novel mixed-triggered filter design for interval type-2 fuzzy nonlinear Markovian jump systems with randomly occurring packet dropouts

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Abstract

This paper is aimed at investigating the problem of mixed-triggered filter design for interval type-2 (IT2) fuzzy nonlinear Markovian jump systems (MJSs) with randomly occurring packet dropouts. First, an IT2 fuzzy nonlinear MJSs model with parameter uncertainties is established by using IT2 fuzzy model, and the fuzzy filter is designed with different premise variables. Second, a novel mixed-triggered scheme is addressed, which can reduce the needless waste of network resources. Then, two Bernoulli stochastic variables are employed, one to randomly switch the different modes of the mixed-triggered scheme, the other to describe the randomly occurring packet dropouts. Next, in order to ensure that IT2 fuzzy filtering error system is asymptotically stable, sufficient conditions are presented. Moreover, the existence conditions for the fuzzy filter are given by the linear matrix inequalities. Finally, simulation results are given to verify the validity of the proposed method.

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References

  1. Huang, C., Bai, H., Liu, X.: H-Infinity state feedback control for a class of networked cascade control systems with uncertain delay. IEEE Trans. Ind. Inform. 6, 62–72 (2010)

    Article  Google Scholar 

  2. Lu, Z., Zhang, F., Wang, L., Xu, F.: Expansion of mixed H2/\(H_{\infty }\) control prototype into networked control systems. Int. J. Model. Identif. Control 28, 78–85 (2017)

    Article  Google Scholar 

  3. Zhang, D., Han, Q.L., Jia, X.: Network-based output tracking control for T–S fuzzy systems using an event-triggered communication scheme. Fuzzy Sets Syst. 273, 26–48 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang, Y.L., Yang, G.H.: Output tracking control for networked control systems with time delay and packet dropout. Int. J. Control 81, 1709–1719 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Wang, Y.L., Wang, T.B., Han, Q.L.: Fault detection filter design for data reconstruction-based continuous-time networked control systems. Inf. Sci. 328, 577–594 (2016)

    Article  MATH  Google Scholar 

  6. Luo, Y., Wang, Z., Wei, G., Alsaadi, F.E.: \(H_{\infty }\) fuzzy fault detection for uncertain 2-D systems under round-robin scheduling protocol. IEEE Trans. Syst. Man Cybern. Syst. 47, 2172–2184 (2017)

    Article  Google Scholar 

  7. Wang, T.L., Zhou, C., Lu, H., He, J.D., Guo, J.: Hybrid scheduling and quantized output feedback control for networked control systems. Int. J. Control Autom. Syst. 16, 197–206 (2018)

    Article  Google Scholar 

  8. Qu, F.L., Hu, B., Guan, Z.H., Wu, Y.H., He, D.X., Zheng, D.F.: Quantized stabilization of wireless networked control systems with packet losses. ISA Trans. 64, 92–97 (2016)

    Article  Google Scholar 

  9. Xiong, J.L., Lam, J., Gao, H.J., Ho, D.W.C.: On robust stabilization of markovian jump systems with uncertain switching probabilities. Automatica 41, 897–903 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  10. Fei, Z.Y., Gao, H.J., Shi, P.: New results on stabilization of markovian jump systems with time delay. Automatica 45, 2300–2306 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Li, F.B., Wu, L.G., Shi, P.: Stochastic stability of semi-Markovian jump systems with mode-dependent delays. Int. J. Robust Nonlinear Control 24, 3317–3330 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  12. Zhang, L.X., Boukas, E.K.: Stability and stabilization of Markovian jump linear systems with partly unknown transition probabilities. Automatica 45, 463–468 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Wu, L.G., Shi, P., Gao, H.J.: State estimation and sliding-mode control of Markovian jump singular systems. IEEE Trans. Autom. Control 55, 1213–1219 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Li, H.Y., Gao, H.J., Shi, P., Zhao, X.D.: Fault-tolerant control of Markovian jump stochastic systems via the augmented sliding mode observer approach. Automatica 50, 1825–1834 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wu, H.N., Cai, K.Y.: Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control. IEEE Trans. Syst. Man Cybern. Syst. Part B (Cybern.) 36, 509–519 (2005)

    Google Scholar 

  16. Shen, H., Xu, S.Y., Zhou, J.P., Lu, J.J.: Fuzzy \(H_{\infty }\) filtering for nonlinear markovian jump neutral systems. Int. J. Syst. Sci. 42, 767–780 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Zhang, H., Shi, Y., Wang, J.: On energy-to-peak filtering for nonuniformly sampled nonlinear systems: a Markovian jump system approach. IEEE Trans. Fuzzy Syst. 22, 212–222 (2014)

    Article  Google Scholar 

  18. He, S.P., Xu, H.L.: Non-fragile finite-time filter design for time-delayed Markovian jumping systems via T–S fuzzy model approach. Nonlinear Dyn. 80, 1159–1171 (2015)

    Article  MATH  Google Scholar 

  19. Gao, X.B., Ren, H.R., Deng, F.Q., Zhou, Q.: Observer-based finite-time \(H_{\infty }\) control for uncertain discrete-time nonhomogeneous Markov jump systems. J. Frankl. Inst. (2019). https://doi.org/10.1016/j.jfranklin.2018.10.031

    MathSciNet  MATH  Google Scholar 

  20. Jiang, B., Karimi, H.R., Kao, Y., Gao, C.: Adaptive control of nonlinear semi-Markovian jump T-S fuzzy systems with immeasurable premise variables via sliding mode observer. IEEE Trans. Cybern. (2018). https://doi.org/10.1109/TCYB.2018.2874166

  21. Sakthivel, R., Sakthivel, R., Nithya, V., Selvaraj, P., Kwon, O.M.: Fuzzy sliding mode control design of Markovian jump systems with time-varying delay. J. Frankl. Inst. 355, 6353–6370 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  22. Mendel, J.M., John, R.I., Liu, F.: Interval type-2 fuzzy logic systems made simple. IEEE Trans. Fuzzy Syst. 14, 808–821 (2006)

    Article  Google Scholar 

  23. Li, H.Y., Wu, C.W., Wu, L.G., Lam, H.K., Gao, Y.B.: Filtering of interval type-2 fuzzy systems with intermittent measurements. IEEE Trans. Cybern. 46, 668–678 (2016)

    Article  Google Scholar 

  24. Liang, Q.L., Mendel, J.M.: Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8, 535–550 (2000)

    Article  Google Scholar 

  25. Li, H.Y., Wu, C.W., Shi, P., Gao, Y.B.: Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. 45, 2378–2389 (2015)

    Article  Google Scholar 

  26. Sola, H.B., Fernandez, J., Hagras, H., Herrera, F., Pagola, M., Barrenechea, E.: Interval type-2 fuzzy sets are generalization of interval-valued fuzzy sets: toward a wider view on their relationship. IEEE Trans. Fuzzy Syst. 23, 1876–1882 (2015)

    Article  Google Scholar 

  27. Huang, J., Ri, M., Wu, D., Ri, S.: Interval type-2 fuzzy logic modeling and control of a mobile two-wheeled inverted pendulum. IEEE Trans. Fuzzy Syst. 26, 2030–2038 (2018)

    Article  Google Scholar 

  28. Castillo, O., Melin, P., Alanis, A., Montiel, O., Sepulveda, R.: Optimization of interval type-2 fuzzy logic controllers using evolutionary algorithms. Soft Comput. 15, 1145–1160 (2011)

    Article  Google Scholar 

  29. Peng, C., Han, Q.L., Yue, D.: To transmit or not to transmit: a discrete event-triggered communication scheme for networked Takagi–Sugeno fuzzy systems. IEEE Trans. Fuzzy Syst. 21, 164–170 (2013)

    Article  Google Scholar 

  30. Liu, J., Yu, Y., Sun, J., Sun, C.Y.: Distributed event-triggered fixed-time consensus for leader–follower multi-agent systems with nonlinear dynamics and uncertain disturbances. Int. J. Robust Nonlinear Control 28, 3543–3559 (2018)

    Article  MATH  Google Scholar 

  31. Lu, Z.D., Ran, G.T., Zhang, G.L., Xu, F.X.: Event-triggered H\(\infty \) fuzzy filtering for networked control systems with quantization and delays. IEEE Access 6, 20231–20241 (2018)

    Article  Google Scholar 

  32. Lu, Z.D., Ran, G.T., Zhang, G.L., Xu, F.X.: Event-based nonfragile H\(\infty \) filter design for networked control systems with interval time-varying delay. J. Control Sci. Eng. 2018, 1–15 (2018)

    MathSciNet  MATH  Google Scholar 

  33. Peng, C., Yang, T.C.: Event-triggered communication and H\(\infty \) control co-design for networked control systems. Automatica 49, 1326–1332 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  34. Liu, J., Zhang, Y.L., Sun, C.Y., Yu, Y.: Fixed-time consensus of multi-agent systems with input delay and uncertain disturbances via event-triggered control. Inf. Sci. 480, 261–272 (2019)

    Article  MathSciNet  Google Scholar 

  35. Ran, G.T., Lu, Z.D., Xu, F.X., Lu, J.X.: Event-triggered dynamic output feedback control for networked T–S fuzzy systems with asynchronous premise variables. IEEE Access 6, 78740–78750 (2018)

    Article  Google Scholar 

  36. Zhang, H.L., Cheng, J., Wang, H.L., Chen, Y.P., Xiang, H.L.: Robust finite-time event-triggered \(H_{\infty }\) boundedness for network-based Markovian jump nonlinear systems. ISA Trans. 63, 32–38 (2016)

    Article  Google Scholar 

  37. Zha, L.J., Fang, J.A., Li, X.F., Liu, J.L.: Event-triggered output feedback H\({\infty }\) control for networked Markovian jump systems with quantizations. Nonlinear Anal. Hybrid Syst. 24, 146–158 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  38. Wang, H.J., Shi, P., Agarwal, R.K.: Network-based event-triggered filtering for Markovian jump systems. Int. J. Control 89, 1096–1110 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  39. Cheng, J., Park, J.H., Zhang, L., Zhu, Y.: An asynchronous operation approach to event-triggered control for fuzzy Markovian jump systems with general switching policies. IEEE Trans. Fuzzy Syst. 26, 6–18 (2018)

    Article  Google Scholar 

  40. Hou, L.Y., Cheng, J., Qi, W.H.: Event-triggered reliable control for fuzzy Markovian jump systems with mismatched membership functions. ISA Trans. 66, 96–104 (2017)

    Article  Google Scholar 

  41. Shen, M.Q., Ye, D., Wang, Q.G.: Event-triggered H\(\infty \) filtering of Markov jump systems with general transition probabilities. Inf. Sci. 418–419, 635–651 (2017)

    Article  Google Scholar 

  42. Kang, W., Cheng, J., Wang, B., Park, J.H., Fardoun, H.M.: Event-triggered reliable control for Markovian jump systems subject to nonuniform sampled data. J. Frankl. Inst. 354, 5877–5894 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  43. Aslam, M.S., Chen, Z.R., Zhang, B.Y.: Event-triggered fuzzy filtering in networked control system for a class of non-linear system with time delays. Int. J. Syst. Sci. 49, 1587–1602 (2018)

    Article  MathSciNet  Google Scholar 

  44. Assawinchaichote, W., Nguang, S.K., Shi, P.: Robust \(H_{\infty }\) fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps: an LMI approach. Inf. Sci. 177, 1699–1714 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  45. Zhang, M., Shi, P., Liu, Z.T., Su, H.Y., Ma, L.H.: Fuzzy model-based asynchronous \(H_{\infty }\) filter design of discrete-time Markov jump systems. J. Frankl. Inst. 354, 8444–8460 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  46. Sathishkumar, M., Sakthivel, R., Kwon, O.M., Kaviarasan, B.: Finite-time mixed \(H_{\infty }\) and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems. Int. J. Syst. Sci. 48, 1416–1427 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  47. Zhang, L.C., Boukas, E.K.: Mode-dependent \(H_{\infty }\) filtering for discrete-time Markovian jump linear systems with partly unknown transition probabilities. Automatica 45, 1462–1467 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  48. Yang, S.H., Wu, J.L.: Mixed event/time-triggered static output feedback l2-gain control for networked control systems. Asian J. Control 19, 1–10 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  49. Liu, J.L., Wei, L.L., Tian, E.G., Fei, S.M., Cao, J.: \(H_{\infty }\) filtering for networked systems with hybrid-triggered communication mechanism and stochastic cyber attacks. J. Frankl. Inst. 354, 8490–8512 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  50. Liu, J., Zhang, Y.L., Sun, C.Y., Yu, Y.: Fixed-time event-triggered consensus for nonlinear multi-agent systems without continuous communications. IEEE Trans. Syst. Man Cybern. Syst. (2018). https://doi.org/10.1109/TSMC.2018.2876334

    Google Scholar 

  51. Ma, S.D., Peng, C., Song, Y., Du, D.J.: Networked \(H_{\infty }\) filtering for markovian jump T–S fuzzy systems with imperfect premise matching. IET Signal Process. 11, 304–312 (2017)

    Article  Google Scholar 

  52. Gu, K., Kharitonov, V.L., Chen, J.: Stability of Time-Delay Systems. Springer, Berlin (2003)

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  54. Wang, H.J., Zhang, D., Lu, R.Q.: Event-triggered \(H_{\infty }\) filter design for Markovian jump systems with quantization. Nonlinear Anal. Hybrid Syst. 28, 23–41 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  55. Lin, C., Wang, Q., Lee, T.H., Chen, B.: \(H_{\infty } \) filter design for nonlinear systems with time-delay through T–S fuzzy model approach. IEEE Trans. Fuzzy Syst. 16, 739–746 (2008)

    Article  Google Scholar 

  56. Hu, S., Lu, Y., Wu, Y., Li, Y.: Partial-information-based consensus of network systems with time-varying delay via sampled-data control. Signal Process. 162, 97–105 (2019)

    Article  Google Scholar 

  57. Xie, X., Yue, D., Peng, C.: Multi-instant observer design of discrete-time fuzzy systems: a ranking-based switching approach. IEEE Trans. Fuzzy Syst. 25, 1281–1292 (2017)

    Article  Google Scholar 

  58. Li, X., Zhang, X., Song, S.: Effect of delayed impulses on input-to-state stability of nonlinear systems. Automatica 76, 378–382 (2017)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This work was supported in part by The Fundamental Research Funds in Heilongjiang Provincial Universities (Nos. 135209241, 135109242, 135309372, 135309505, and 135309506), Heilongjiang Province Natural Science Foundation (No. F2017028), and China Natural Science Foundation (No. 61672304).

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Authors and Affiliations

  1. College of Computer and Control Engineering, Qiqihar University, Qiqihar, 161006, People’s Republic of China

    Zhongda Lu, Guangtao Ran, Fengxia Xu & Junxiao Lu

  2. College of Computer Science and Technology, Harbin University of Science and Technology, Harbin, 158080, People’s Republic of China

    Zhongda Lu

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  1. Zhongda Lu
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Lu, Z., Ran, G., Xu, F. et al. Novel mixed-triggered filter design for interval type-2 fuzzy nonlinear Markovian jump systems with randomly occurring packet dropouts. Nonlinear Dyn 97, 1525–1540 (2019). https://doi.org/10.1007/s11071-019-05070-x

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