Skip to main content
SpringerLink
Log in

An Event-Triggered \({H_\infty }\) Filter for Interval Type-2 T–S Fuzzy Nonlinear Networked Systems with Parameter Uncertainties and Delays

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

This paper designs an event-triggered \({H_\infty }\) filter for interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy nonlinear networked systems with parameter uncertainties and delays. First, an IT2 T–S fuzzy model is used to describe the nonlinear plant and the filter subject to parameter uncertainties, which can be captured with the lower and upper membership functions. Then, an event-triggered scheme and a quantizer are proposed to reduce the unnecessary waste of the network resources. Second, the asynchronous premise variables problem is considered in the design of the fuzzy filter, which means that the premise variable of the designed filter needs not to be identical with the plant. Third, by constructing a Lyapunov–Krasovskii function with quadruple integral items, and employing the Wirtinger inequality and some slack matrices, a stability condition with less conservative is obtained. Finally, a numerical example demonstrates the effectiveness of the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  1. Liu, A., Zhang, W.A., Yu, L., Liu, S., Chen, M.Z.Q.: New results on stabilization of networked control systems with packet disordering. Automatica 52, 255–259 (2015)

    MathSciNet  MATH  Google Scholar 

  2. Qiu, J., Gao, H., Ding, S.X.: Recent advances on fuzzy-model-based nonlinear networked control systems: a survey. IEEE Trans. Industr. Electron. 63, 1207–1217 (2016)

    Google Scholar 

  3. Zhang, X.M., Han, Q.L., Yu, X.: Survey on recent advances in networked control systems. IEEE Trans. Industr. Inf. 12, 1740–1752 (2016)

    Google Scholar 

  4. Wang, Y.L., Han, Q.L.: Network-based modelling and dynamic output feedback control for unmanned marine vehicles in network environments. Automatica. 91, 43–53 (2018)

    MathSciNet  MATH  Google Scholar 

  5. Islam, S., Liu, P.X., El Saddik, A.: Robust control of four-rotor unmanned aerial vehicle with disturbance uncertainty. IEEE Trans. Industr. Electron. 62, 1563–1571 (2015)

    Google Scholar 

  6. Ran, G., Liu, J., Li, C., Chen, L., Li, D.: Event-based finite-time consensus control of second-order delayed multi-agent systems. IEEE Trans. Circ. Syst. II Express Briefs 68(1), 276–280 (2021). https://doi.org/10.1109/TCSII.2020.2999480

    Article  Google Scholar 

  7. Zhang, L., Gao, H., Kaynak, O.: Network-induced constraints in networked control systems: a survey. IEEE Trans. Industr. Inf. 9, 403–416 (2013)

    Google Scholar 

  8. Gupta, R.A., Chow, M.Y.: Networked control system: overview and research trends. IEEE Trans. Industr. Electron. 57, 2527–2535 (2010)

    Google Scholar 

  9. Hespanha, J.P., Naghshtabrizi, P., Xu, Y.: A survey of recent results in networked control systems. Proc. IEEE 95, 138–162 (2007)

    Google Scholar 

  10. Peng, C., Yue, D., Tian, E., Gu, Z.: A delay distribution based stability analysis and synthesis approach for networked control systems. J. Franklin Inst. 346(4), 349–365 (2009)

    MathSciNet  MATH  Google Scholar 

  11. Dai, S.L., Lin, H., Ge, S.S.: Scheduling-and-control code sign for a collection of networked control systems with uncertain delays. IEEE Trans. Control Syst. Technol. 18(1), 66–78 (2009)

    Google Scholar 

  12. Sun, S., Ma, J.: Linear estimation for networked control systems with random transmission delays and packet dropouts. Inf. Sci. 269, 349–365 (2014)

    MathSciNet  MATH  Google Scholar 

  13. Zhang, B., Zheng, W.X., Xu, S.: Filtering of Markovian jump delay systems based on a new performance index. IEEE Trans. Circ. Syst. I Regul. Pap. 60(5), 1250–1263 (2013)

    MathSciNet  MATH  Google Scholar 

  14. Zhang, X.M., Han, Q.L.: Network-based filtering for discrete-time systems. IEEE Trans. Signal Process. 60(2), 956–961 (2012)

    MathSciNet  MATH  Google Scholar 

  15. Qiu, J.B., Sun, K., Rudas, I.J., Gao, H.: Command filter-based adaptive NN control for MIMO nonlinear systems with full-state constraints and actuator hysteresis. IEEE Trans. Cybern. 50(7), 2905–2915 (2020)

    Google Scholar 

  16. Tseng, C.S., Chen, B.S., Uang, H.J.: Fuzzy tracking control design for nonlinear dynamic systems via T-S fuzzy model. IEEE Trans. Fuzzy Syst. 9(3), 381–392 (2001)

    Google Scholar 

  17. Fang, C.H., Liu, Y.S., Kau, S.W., Hong, L., Lee, C.H.: A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems. IEEE Trans. Fuzzy Syst. 14(3), 386–397 (2006)

    Google Scholar 

  18. Ren, H., Chen, L., Zhou, Q.: Fuzzy control for uncertain electric vehicle systems with sensor failures and actuator saturation. Int. J. Fuzzy Syst. 22, 1444–1453 (2020)

    Google Scholar 

  19. Li, B., Xia, J., Zhang, H., Shen, H., Wang, Z.: Event-triggered adaptive fuzzy tracking control for nonlinear systems. Int. J. Fuzzy Syst. 22, 1389–1399 (2020)

    MATH  Google Scholar 

  20. Fan, Y., An, Y., Wang, W., Yang, C.: T-S fuzzy adaptive control based on small gain approach for an uncertain robot manipulators. Int. J. Fuzzy Syst. (2020). https://doi.org/10.1007/s40815-019-00793-w

    Article  Google Scholar 

  21. Wang, Z., Zhao, Y., Du, H., Cao, K.: Stability analysis of TS fuzzy control systems subject to actuator saturation. Int. J. Fuzzy Syst. 21(8), 2625–2631 (2019)

    MathSciNet  Google Scholar 

  22. Chang, X.H., Yang, G.H.: Nonfragile \(H_ {\infty }\) filter design for TS fuzzy systems in standard form. IEEE Trans. Industr. Electron. 61(7), 3448–3458 (2013)

    Google Scholar 

  23. Wei, Y., Qiu, J., Shi, P., Lam, H.K.: A New design of \(H_\infty\) piecewise filtering for discrete-time nonlinear time-varying delay systems via T-S fuzzy affine models. IEEE Trans. Syst. Man Cybern. Syst. 47(8), 2034–2047 (2016)

    Google Scholar 

  24. Lu, R., Cheng, H., Bai, J.: Fuzzy-model-based quantized guaranteed cost control of nonlinear networked systems. IEEE Trans. Fuzzy Syst. 23(3), 567–575 (2014)

    Google Scholar 

  25. Liang, Q., Mendel, J.M.: Interval type-2 fuzzy logic systems: theory and design. IEEE Trans. Fuzzy Syst. 8(5), 535–550 (2000)

    Google Scholar 

  26. Lam, H., Li, H., Deters, C., Secco, E.L., Wurdemann, H.A., Althoefer, K.: Control design for interval type-2 fuzzy systems under imperfect premise matching. IEEE Trans. Industr. Electron. 61(2), 956–968 (2014)

    Google Scholar 

  27. Li, H., Wu, C., Wu, L., Lam, H.K., Gao, Y.: Filtering of interval type-2 fuzzy systems with intermittent measurements. IEEE Trans. Cybern. 46(3), 668–678 (2015)

    Google Scholar 

  28. Li, H., Pan, Y., Zhou, Q.: Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. 23(3), 719–725 (2014)

    Google Scholar 

  29. Ran, G., Li, C.: Membership-function-dependent approach to design filter for nonlinear systems with time-varying delay via interval type-2 fuzzy model. IET Control Theory Appl. 15(4), 512–522 (2021). https://doi.org/10.1049/cth2.12056

    Article  Google Scholar 

  30. Chen, T.Y.: An ELECTRE-based outranking method for multiple criteria group decision making using interval type-2 fuzzy sets. Inf. Sci. 263, 1–21 (2014)

    MathSciNet  MATH  Google Scholar 

  31. Castillo, O., Melin, P.: A review on interval type-2 fuzzy logic applications in intelligent control. Inf. Sci. 279, 615–631 (2014)

    MathSciNet  MATH  Google Scholar 

  32. Ghorabaee, M.K.: Developing an MCDM method for robot selection with interval type-2 fuzzy sets. Robot. Comput. Integr. Manufact. 37, 221–232 (2016)

    Google Scholar 

  33. Li, H., Wang, J., Lam, H.K., Zhou, Q., Du, H.: Adaptive sliding mode control for interval type-2 fuzzy systems. IEEE Trans. Syst. Man Cybernet. Syst. 46(12), 1654–1663 (2016)

    Google Scholar 

  34. Lu, Q., Shi, P., Lam, H.K., Zhao, Y.: Interval type-2 fuzzy model predictive control of nonlinear networked control systems. IEEE Trans. Fuzzy Syst. 23(6), 2317–2328 (2015)

    Google Scholar 

  35. Liu, J., Yu, Y., He, H., Sun, C.: Team-triggered practical fixed-time consensus of double-integrator agents with uncertain disturbance. IEEE Trans. Cybern. 51(6), 3263–3272 (2021). https://doi.org/10.1109/TCYB.2020.2999199

    Article  Google Scholar 

  36. Qiu, J.B., Sun, K., Wang, T., Gao, H.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 27(11), 2152–2162 (2019)

    Google Scholar 

  37. Liu, J., Zhang, Y., Yu, Y., Sun, C.: Fixed-time event-triggered consensus for nonlinear multiagent systems without continuous communications. IEEE Trans. Syst. Man Cybern. Syst. 49(11), 2221–2229 (2019)

    Google Scholar 

  38. Liu, J., Zhang, Y., Yu, Y., Sun, C.: Fixed-time leader-follower consensus of networked nonlinear systems via event/self-triggered control. IEEE Trans. Neural Netw. Learn. Syst. 31(11), 5029–5037 (2020)

    MathSciNet  Google Scholar 

  39. Lu, Z., Ran, G., Xu, F., Lu, J.: Novel mixed-triggered filter design for interval type-2 fuzzy nonlinear Markovian jump systems with randomly occurring packet dropouts. Nonlinear Dyn. 97(2), 1525–1540 (2019)

    MATH  Google Scholar 

  40. Yu, H., Antsaklis, P.J.: Event-triggered output feedback control for networked control systems using passivity: achieving L2 stability in the presence of communication delays and signal quantization. Automatica. 49(1), 30–38 (2013)

    MathSciNet  MATH  Google Scholar 

  41. Li, H., Chen, Z., Wu, L., Lam, H.K., Du, H.: Event-triggered fault detection of nonlinear networked systems. IEEE Trans. Cybern. 47(4), 1041–1052 (2016)

    Google Scholar 

  42. 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)

    Google Scholar 

  43. Ding, L., Guo, G.: Distributed event-triggered \(H_\infty\) consensus filtering in sensor networks. Sig. Process. 108, 365–375 (2015)

    Google Scholar 

  44. Postoyan, R., Bragagnolo, M.C., Galbrun, E., Daafouz, J., Nešić, D., Castelan, E.B.: Event-triggered tracking control of unicycle mobile robots. Automatica. 52, 302–308 (2015)

    MathSciNet  MATH  Google Scholar 

  45. Cheng, Y., Ugrinovskii, V.: Event-triggered leader-following tracking control for multivariable multi-agent systems. Automatica. 70, 204–210 (2016)

    MathSciNet  MATH  Google Scholar 

  46. Peng, C., Yang, T.C.: Event-triggered communication and \(H_\infty\) control co-design for networked control systems. Automatica. 49(5), 1326–1332 (2013)

    MathSciNet  MATH  Google Scholar 

  47. Huang, S.J., He, X.Q., Zhang, N.N.: New results on \(H_\infty\) filter design for nonlinear systems with time delay via T-S fuzzy models. IEEE Trans. Fuzzy Syst. 19(1), 193–199 (2010)

    Google Scholar 

  48. Pan, Y., Yang, G.H.: Novel event-triggered filter design for nonlinear networked control systems. J. Franklin Inst. 355(3), 1259–1277 (2018)

    MathSciNet  MATH  Google Scholar 

  49. Lam, H., Seneviratne, L.: Stability analysis of interval type-2 fuzzy-model-based control systems. IEEE Trans. Syst. Man Cybernet. Part B (Cybern.) 38(3), 617–628 (2008)

    Google Scholar 

  50. Pan, Y., Yang, G.H.: Event-triggered fuzzy control for nonlinear networked control systems. Fuzzy Sets Syst. 329, 91–107 (2017)

    MathSciNet  MATH  Google Scholar 

  51. Pan, Y., Yang, G.H.: Event-triggered fault detection filter design for nonlinear networked systems. IEEE Trans. Syst. Man Cybern. Syst. 48(11), 1851–1862 (2017)

    Google Scholar 

  52. Hu, S., Yue, D., Xie, X., Du, Z.: Event-triggered \(H_\infty\) stabilization for networked stochastic systems with multiplicative noise and network-induced delays. Inf. Sci. 299, 178–197 (2015)

    MathSciNet  MATH  Google Scholar 

  53. Seuret, A., Gouaisbaut, F.: On the use of the Wirtinger inequalities for time-delay systems. IFAC Proc. Vol. 45(14), 260–265 (2012)

    Google Scholar 

  54. Petersen, I.R.: A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. 8(4), 351–357 (1987)

    MathSciNet  MATH  Google Scholar 

  55. Wang, H., Shi, P., Zhang, J.: Event-triggered fuzzy filtering for a class of nonlinear networked control systems. Sig. Process. 113, 159–168 (2015)

    Google Scholar 

  56. Lin, C., Wang, Q.G., 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(3), 739–746 (2008)

    Google Scholar 

  57. Zhang, J., Peng, C.: Networked \(H_\infty\) filtering under a weighted TOD protocol. Automatica. 107, 333–341 (2019)

    MathSciNet  MATH  Google Scholar 

  58. Liu, X., Su, X., Shi, P., Nguang, S.K., Shen, C.: Fault detection filtering for nonlinear switched systems via event-triggered communication approach. Automatica 101, 365–376 (2019)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Control Science and Engineering, Harbin Institute of Technology, Harbin, 150001, China

    Guangtao Ran

  2. Key Laboratory of Advanced Perception and Intelligent Control of High-end Equipment of Ministry of Education, Anhui Polytechnic University, Wuhu, 241000, China

    Guangtao Ran, Jian Liu & Yiqing Huang

  3. School of Cyber Science and Technology, Beihang University, Beijing, 100191, China

    Dongyu Li

  4. School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, 100083, China

    Yanling Zhang

  5. School of Automation, Southeast University, Nanjing, 210096, China

    Jian Liu

Authors
  1. Guangtao Ran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dongyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yanling Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yiqing Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yanling Zhang.

Ethics declarations

Disclosure statement

No potenttial conflict of interest was reported by the authors.

Funding

This work was supported by the National Natural Science Foundation of China under Grants 61876050 and 62033010,the Opening Project of Key Laboratory of Advanced Perception and Intelligent Control of Highend Equipment of Ministry of Education, Anhui Polytechnic University under Grant GDSC202004, the Fundamental Research Funds for the Central Universities under Grant 2242021R20002, theUniversity Synergy Innovation Program of Anhui Province under Grant GXXT-2020-069, the China Postdoctoral Science Foundation funded project under Grant 2020M681449, the Natural Science Foundation of Jiangsu Province under GrantBK20200239,and the Equipment Pre-research Field Fund under GrantJZX7Y20190243001201. 

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ran, G., Liu, J., Li, D. et al. An Event-Triggered \({H_\infty }\) Filter for Interval Type-2 T–S Fuzzy Nonlinear Networked Systems with Parameter Uncertainties and Delays. Int. J. Fuzzy Syst. 23, 2144–2156 (2021). https://doi.org/10.1007/s40815-021-01083-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-021-01083-0

Keywords

Search

Navigation