Skip to main content
SpringerLink
Log in

Dissipative Filtering of Markovian Jumping Systems via Adaptive Sliding Mode Control

  • Published:
Circuits, Systems, and Signal Processing Aims and scope Submit manuscript

Abstract

In this study, dissipative filtering of Markovian jumping systems (MJSs) is investigated using the sliding mode control (SMC) method. A novel dynamic model considering linearity and nonlinearity was proposed, and an adaptive sliding motion controller was established to study the dissipation and mean-square exponential stability. First, MJSs with time-varying delays are proposed, which involve known and unknown nonlinear functions. Subsequently, a novel sliding mode surface (SMS) function was constructed to ensure that the trajectory of the sliding motion dynamics could move along the SMS. In addition, an appropriate SMC rule was presented to guarantee SMS accessibility. Second, the filter was obtained through dissipation theory, which ensures that the filtering error system is extended-dissipative and the mean-square is exponentially stable. Finally, the effectiveness of this method was verified using a practical example.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Data Availability

Data sharing is not applicable to this article as no data sets were generated or analysed during the current study.

References

  1. L. An, G.H. Yang, Distributed optimal coordination for heterogeneous linear multiagent systems. IEEE Trans. Autom. Control 67(12), 6850–6857 (2021)

    Article  MathSciNet  Google Scholar 

  2. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear matrix inequalities in system and control theory (SIAM, Philadelphia, 1994)

    Book  Google Scholar 

  3. L. Cao, Y. Pan, H. Liang, T. Huang, Observer-based dynamic event-triggered control for multiagent systems with time-varying delay. IEEE Trans. Cybern. 53(5), 3376–3387 (2022)

    Article  Google Scholar 

  4. K. Ding, Q. Zhu, Extended dissipative anti-disturbance control for delayed switched singular semi-Markovian jump systems with multi-disturbance via disturbance observer. Automatica 128, 109556 (2021)

    Article  MathSciNet  Google Scholar 

  5. Y. Han, S. Zhou, Extended dissipative filtering for Markovian jump interval-valued fuzzy systems with uncertain transition rates. Fuzzy Sets Syst. 416, 86–107 (2021)

    Article  MathSciNet  Google Scholar 

  6. Y. Han, S. Zhou, Line integral approach to extended dissipative filtering for interval type-2 fuzzy systems. IEEE Trans. Cybern. 52(5), 3757–3768 (2022)

    Article  Google Scholar 

  7. D.W. Ho, Y. Niu, Robust fuzzy design for nonlinear uncertain stochastic systems via sliding-mode control. IEEE Trans. Fuzzy Syst. 15(3), 350–358 (2007)

    Article  Google Scholar 

  8. B. Jiang, H.R. Karimi, Y. Kao, C. Gao, A novel robust fuzzy integral sliding mode control for nonlinear semi-Markovian jump T-S fuzzy systems. IEEE Trans. Fuzzy Syst. 26(6), 3594–3604 (2018)

    Article  Google Scholar 

  9. B. Jiang, H.R. Karimi, S. Yang, C. Gao, Y. Kao, Observer-based adaptive sliding mode control for nonlinear stochastic Markov jump systems via T-S fuzzy modeling: applications to robot arm model. IEEE Trans. Ind. Electron. 68(1), 466–477 (2020)

    Article  Google Scholar 

  10. N. Krasovskii, E. Lidskii, Analytical design of controllers in systems with random attributes. Autom. Remote. Control. 22(1–3), 1021–1025 (1961)

    Google Scholar 

  11. H. Li, P. Shi, D. Yao, L. Wu, Observer-based adaptive sliding mode control for nonlinear Markovian jump systems. Automatica 64, 133–142 (2016)

    Article  MathSciNet  Google Scholar 

  12. Y. Li, Y. Zhao, W. Liu, J. Hu, Adaptive fuzzy predefined-time control for third-order heterogeneous vehicular platoon systems with dead-zone. IEEE Trans. Industr. Inf. 19(9), 9525–9534 (2023)

    Article  Google Scholar 

  13. H. Liang, L. Chen, Y. Pan, H.K. Lam, Fuzzy-based robust precision consensus tracking for uncertain networked systems with cooperative-antagonistic interactions. IEEE Trans. Fuzzy Syst. 31(4), 1362–1376 (2022)

    Article  Google Scholar 

  14. G. Liu, S. Xu, J.H. Park, G. Zhuang, Reliable exponential filtering for singular Markovian jump systems with time-varying delays and sensor failures. Int. J. Robust Nonlinear Control 28(14), 4230–4245 (2018)

    Article  MathSciNet  Google Scholar 

  15. D. Lu, D. Tong, Q. Chen, W. Zhou, J. Zhou, S. Shen, Exponential synchronization of stochastic neural networks with time-varying delays and lévy noises via event-triggered control. Neural Process. Lett. 53, 2175–2196 (2021)

    Article  Google Scholar 

  16. R. Lu, J. Tao, P. Shi, H. Su, Z.G. Wu, Y. Xu, Dissipativity-based resilient filtering of periodic Markovian jump neural networks with quantized measurements. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1888–1899 (2017)

    Article  MathSciNet  Google Scholar 

  17. M. Sathishkumar, R. Sakthivel, O. Kwon, B. Kaviarasan, Finite-time mixed \({H}_{\infty }\) and passive filtering for Takagi–Sugeno fuzzy nonhomogeneous Markovian jump systems. Int. J. Syst. Sci. 48(7), 1416–1427 (2017)

    Article  MathSciNet  Google Scholar 

  18. S. Sun, H. Zhang, J. Han, J. Zhang, Dissipativity-based finite-time filtering for uncertain semi-Markovian jump random systems with multiple time delays and state constraints. IEEE Trans. Neural Netw. Learn. Syst. 33(7), 2995–3009 (2021)

    Article  MathSciNet  Google Scholar 

  19. Y. Tian, Z. Wang, A new integral inequality approach for extended dissipative filters design of singular Markovian jump systems with discrete and distributed delays. Circuits Syst. Sig. Process 39, 2900–2921 (2020)

    Article  Google Scholar 

  20. Y. Tian, Z. Wang, Asynchronous extended dissipative filtering for T-S fuzzy Markov jump systems. IEEE Trans. Syst. Man Cybern. Syst. 52(6), 3915–3925 (2022)

    Article  Google Scholar 

  21. D. Tong, X. Liu, Q. Chen, W. Zhou, K. Liao, Observer-based adaptive finite-time prescribed performance NN control for nonstrict-feedback nonlinear systems. Neural Comput. Appl. 34(15), 12789–12805 (2022)

    Article  Google Scholar 

  22. D. Tong, B. Ma, Q. Chen, Y. Wei, P. Shi, Finite-time synchronization and energy consumption prediction for multilayer fractional-order networks. IEEE Trans. Circuits Syst. Express Briefs 70(6), 2176–2180 (2023)

    Article  Google Scholar 

  23. D. Tong, C. Xu, Q. Chen, W. Zhou, Y. Xu, Sliding mode control for nonlinear stochastic systems with Markovian jumping parameters and mode-dependent time-varying delays. Nonlinear Dyn. 100(2), 1343–1358 (2020)

    Article  Google Scholar 

  24. J.C. Willems, Dissipative dynamical systems part I: general theory. Arch. Ration. Mech. Anal. 45(5), 321–351 (1972)

    Article  Google Scholar 

  25. C. Xu, D. Tong, Q. Chen, W. Zhou, P. Shi, Exponential stability of Markovian jumping systems via adaptive sliding mode control. IEEE Trans. Syst. Man Cybern. Syst. 51(2), 954–964 (2021)

    Article  Google Scholar 

  26. Y. Xu, Z.G. Wu, Y.J. Pan, Event-based dissipative filtering of Markovian jump neural networks subject to incomplete measurements and stochastic cyber-attacks. IEEE Trans. Cybern. 51(3), 1370–1379 (2019)

    Article  Google Scholar 

  27. G. Yang, D. Tong, Q. Chen, W. Zhou, Fixed-time synchronization and energy consumption for Kuramoto-oscillator networks with multilayer distributed control. IEEE Trans. Circuits Syst. Express Briefs 70(4), 1555–1559 (2023)

    Article  Google Scholar 

  28. J. Yang, W. Zhou, P. Shi, X. Yang, X. Zhou, H. Su, Adaptive synchronization of delayed Markovian switching neural networks with Lévy noise. Neurocomputing 156, 231–238 (2015)

    Article  Google Scholar 

  29. J. Yang, W. Zhou, P. Shi, X. Yang, X. Zhou, H. Su, Synchronization of delayed neural networks with Lévy noise and Markovian switching via sampled data. Nonlinear Dyn. 81(3), 1179–1189 (2015)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  31. G. Zhang, D. Tong, Q. Chen, W. Zhou, Sliding mode control against false data injection attacks in dc microgrid systems. IEEE Syst. J. (2023). https://doi.org/10.1109/JSYST.2023.3280185

    Article  Google Scholar 

  32. J. Zhang, X. Liu, Y. Xia, Z. Zuo, Y. Wang, Disturbance observer-based integral sliding-mode control for systems with mismatched disturbances. IEEE Trans. Ind. Electron. 63(11), 7040–7048 (2016)

    Article  Google Scholar 

  33. L. Zhang, C. Deng, W.W. Che, L. An, Adaptive backstepping control for nonlinear interconnected systems with prespecified-performance-driven output triggering. Automatica 154, 111063 (2023)

    Article  MathSciNet  Google Scholar 

  34. L. Zhang, Y. Sun, Y. Pan, D. Hou, S. Wang, Network-based robust event-triggered control for continuous-time uncertain semi-Markov jump systems. Int. J. Robust Nonlinear Control 31(1), 306–323 (2021)

    Article  MathSciNet  Google Scholar 

  35. L. Zhang, Y. Sun, Y. Pan, H.K. Lam, Reduced-order fault detection filter design for fuzzy semi-Markov jump systems with partly unknown transition rates. IEEE Trans. Syst. Man, Cybern. Syst. 52(12), 7702–7713 (2022)

    Article  Google Scholar 

  36. Q. Zhang, J. Zhang, Y. Wang, Sliding-mode control for singular Markovian jump systems with Brownian motion based on stochastic sliding mode surface. IEEE Trans. Syst. Man Cybern. Syst. 49(3), 494–505 (2017)

    Article  Google Scholar 

  37. Y. Zhang, C. Ding, J. Wang, J. Cao, High-energy orbit sliding mode control for nonlinear energy harvesting. Nonlinear Dyn. 105(1), 191–211 (2021)

    Article  Google Scholar 

  38. J. Zhao, D.J. Hill, Dissipativity theory for switched systems. IEEE Trans. Autom. Control 53(4), 941–953 (2008)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is partially supported by the Guangxi Natural Science Foundation under Grant No. 2023GXNSFAA026104, Zhejiang Provincial Natural Science Foundation of China under Grant LZ22F020002, and Huzhou Science and Technology Planning Foundation under Grant No. 2023GZ04.

Author information

Authors and Affiliations

  1. College of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Guoqing Zhai & Qiaoyu Chen

  2. College of Information Engineering, Guangxi City Vocational University, Nanning, 532100, Guangxi, China

    Dongbing Tong

  3. College of Information Sciences and Technology, Donghua University, Shanghai, 200051, China

    Wuneng Zhou

  4. School of Information Engineering, Huzhou University, Huzhou, 313000, China

    Shigen Shen

Authors
  1. Guoqing Zhai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qiaoyu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dongbing Tong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wuneng Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Shigen Shen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Qiaoyu Chen or Dongbing Tong.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhai, G., Chen, Q., Tong, D. et al. Dissipative Filtering of Markovian Jumping Systems via Adaptive Sliding Mode Control. Circuits Syst Signal Process 43, 865–894 (2024). https://doi.org/10.1007/s00034-023-02520-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-023-02520-1

Keywords

Search

Navigation