Nothing Special   »   [go: up one dir, main page]
Skip to main content
Springer Nature Link
Log in

Adaptive Event-Triggered \(H_{\infty }\) Control for Markov Jump Systems with Generally Uncertain Transition Rates

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

Abstract

This paper considers the adaptive event-triggered \(H_{\infty }\) control issue for Markov jump systems with generally uncertain transition rates and actuator faults. Compared with the conventional method, an adaptive event-triggered mechanism with a varying threshold is adopted to save the communication resources effectively. The general model of transition rates in Markov jump process includes completely unknown and uncertain bounded as two special models. Based on linear matrix inequalities, the sufficient conditions of the controller design can be obtained to guarantee the closed-loop systems are stochastically stable. Finally, simulation examples are exploited to verify the effectiveness of the proposed control strategy.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. W. Bai, Q. Zhou, T. Li, H. Li, Adaptive reinforcement learning neural network control for uncertain nonlinear system with input saturation. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.292105

    Article  Google Scholar 

  2. W. Bai, B. Zhang, Q. Zhou, R. Lu, Multigradient recursive reinforcement learning NN control for affine nonlinear systems with unmodeled dynamics. Int. J. Robust Nonlinear Control (2019). https://doi.org/10.1002/rnc.4843

    Article  Google Scholar 

  3. L. Cao, H. Li, G. Dong, R. Lu, Event-triggered control for multi-agent systems with sensor faults and input saturation. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2938216

    Article  Google Scholar 

  4. L. Chen, X. Li, W. Xiao, P. Li, Q. Zhou, Fault-tolerant control for uncertain vehicle active steering systems with time-delay and actuator fault. Int. J. Control Autom. Syst. 17(9), 2234–2241 (2019)

    Google Scholar 

  5. L. Chen, P. Li, W. Lin, Q. Zhou, Observer-based fuzzy control for four-wheel independently driven electric vehicles with active steering systems. Int. J. Fuzzy Syst. 22(1), 89–100 (2020)

    MathSciNet  Google Scholar 

  6. Z.Y. Chen, Q.L. Han, Y.M. Yan, Z.G. Wu, How often should one update control and estimation: review of networked triggering techniques. Sci. China Inf. Sci. 63(5), 150201 (2020)

    MathSciNet  Google Scholar 

  7. G. Dong, H. Li, H. Ma, R. Lu, Finite-time consensus tracking neural network FTC of multi-agent systems. IEEE Trans. Neural Netw. Learn. Syst. (2020). https://doi.org/10.1109/TNNLS.2020.2978898

    Article  Google Scholar 

  8. M.C.F. Donkers, W.P.M.H. Heemels, N.V.D. Wouw, L. Hetel, Stability analysis of networked control systems using a switched linear systems approach. IEEE Trans. Autom. Control. 56(9), 2101–2115 (2011)

    MathSciNet  MATH  Google Scholar 

  9. P. Du, H. Liang, S. Zhao, C.K. Ahn, Neural-based decentralized adaptive finite-time control for nonlinear large-scale systems with time-varying output constraints. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2918351

    Article  Google Scholar 

  10. Q.Y. Fan, G.H. Yang, D. Ye, Adaptive tracking control for a class of Markovian jump systems with time-varying delay and actuator faults. J. Frankl. Inst. 352(5), 1979–2001 (2015)

    MathSciNet  MATH  Google Scholar 

  11. X. Gao, F. Deng, X. Li, Q. Zhou, Event-triggered finite-time reliable control for nonhomogeneous Markovian jump systems. Int. J. Robust Nonlinear Control (2019). https://doi.org/10.1002/rnc.4858

    Article  Google Scholar 

  12. X. Gao, H. Ren, F. Deng, Q. Zhou, Observer-based finite-time \(H_{\infty }\) control for uncertain discrete-time nonhomogeneous Markov jump systems. J. Frankl. Inst. 356, 1730–1749 (2019)

    MathSciNet  MATH  Google Scholar 

  13. Z. Gu, D. Yue, J. Liu, Z. Ding, \(H_{\infty }\) tracking control of nonlinear networked systems with a novel adaptive event-triggered communication scheme. J. Frankl. Inst. 354(8), 3540–3553 (2017)

    MathSciNet  MATH  Google Scholar 

  14. Z. Gu, E. Tian, J. Liu, Adaptive event-triggered control of a class of nonlinear networked systems. J. Frankl. Inst. 354(9), 3854–3871 (2017)

    MathSciNet  MATH  Google Scholar 

  15. Y. Guo, Z. Wang, Stability of Markovian jump systems with generally uncertain transition rates. J. Frankl. Inst. 350(9), 2826–2836 (2013)

    MathSciNet  MATH  Google Scholar 

  16. S. Hu, D. Yue, Event-based \(H_{\infty }\) filtering for networked system with communication delay. Signal Process. 92(9), 2029–2039 (2012)

    Google Scholar 

  17. M. Ji, Z. Li, B. Yang, W. Zhang, Stabilization of Markov jump linear systems with input quantization. Circuits Syst. Signal Process. 34(7), 2109–2126 (2015)

    MathSciNet  MATH  Google Scholar 

  18. B. Jiang, Y. Kao, C. Gao, X. Yao, Passification of uncertain singular semi-Markovian jump systems with actuator failures via sliding mode approach. IEEE Trans. Autom. Control 62(8), 4138–4143 (2017)

    MathSciNet  MATH  Google Scholar 

  19. Y. Kao, J. Xie, C. Wang, Stabilization of singular Markovian jump systems with generally uncertain transition rates. IEEE Trans. Autom. Control 59(9), 2604–2610 (2014)

    MathSciNet  MATH  Google Scholar 

  20. Y. Kao, C. Wang, J. Xie, H.R. Karimi, New delay-dependent stability of Markovian jump neutral stochastic systems with general unknown transition rates. Int. J. Syst. Sci. 47(11), 2499–2509 (2016)

    MathSciNet  MATH  Google Scholar 

  21. H. Li, Y. Shi, Event-triggered robust model predictive control of continuous-time nonlinear systems. Automatica 50(5), 1507–1513 (2014)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  23. H. Li, P. Shi, D. Yao, Adaptive sliding-mode control of Markov jump nonlinear systems with actuator faults. IEEE Trans. Autom. Control 62(4), 1933–1939 (2017)

    MathSciNet  MATH  Google Scholar 

  24. H. Li, Z. Zhang, H. Yan, X. Xie, Adaptive event-triggered fuzzy control for uncertain active suspension systems. IEEE Trans. Cybern. 49(12), 4388–4397 (2019)

    Google Scholar 

  25. H. Li, Y. Wu, M. Chen, Adaptive fault-tolerant tracking control for discrete-time multi-agent systems via reinforcement learning algorithm. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2982168

    Article  Google Scholar 

  26. X. Li, Q. Zhou, P. Li, H. Li, R. Lu, Event-triggered consensus control for multi-agent systems against false data-injection attacks. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2937951

    Article  Google Scholar 

  27. X. Li, B. Zhang, P. Li, Q. Zhou, R. Lu, Finite-horizon \({H}_{\infty }\) state estimation for periodic neural networks over fading channels. IEEE Trans. Neural Netw. Learn. Syst. (2019). https://doi.org/10.1109/TNNLS.2019.2920368

    Article  Google Scholar 

  28. H. Liang, L. Zhang, Y. Sun, T. Huang, Containment control of semi-Markovian multiagent systems with switching topologies. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2946248

    Article  Google Scholar 

  29. H. Liang, X. Guo, Y. Pan, T. Huang, Event-triggered fuzzy bipartite tracking control for network systems based on distributed reduced-order observers. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2982618

    Article  Google Scholar 

  30. Q. Liu, J. Leng, D. Yan, D. Zhang, L. Wei, A. Yu, R. Zhao, H. Zhang, X. Chen, Digital twin-based designing of the configuration, motion, control, and optimization model of a flow-type smart manufacturing system. J. Manuf. Syst. (2020). https://doi.org/10.1016/j.jmsy.2020.04.012

  31. Y. Liu, X. Liu, Y. Jing, H. Wang, X. Li, Annular domain finite-time connective control for large-scale systems with expanding construction. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2960009

    Article  Google Scholar 

  32. X. Luan, C. Zhao, F. Liu, Finite-time stabilization of switching Markov jump systems with uncertain transition rates. Circuits Syst. Signal Process. 34(12), 3741–3756 (2015)

    MathSciNet  MATH  Google Scholar 

  33. Q. Ma, S. Xu, Y. Zou, Stability and synchronization for Markovian jump neural networks with partly unknown transition probabilities. Neurocomputing 74(17), 3404–3411 (2011)

    Google Scholar 

  34. Z. Ning, J. Yu, Y. Pan, H. Li, Adaptive event-triggered fault detection for fuzzy stochastic systems with missing measurements. IEEE Trans. Fuzzy Syst. 26(4), 2201–2212 (2017)

    Google Scholar 

  35. Y. Pan, G.H. Yang, Event-triggered fault detection filter design for nonlinear networked systems. IEEE Trans. Syst. Man Cybern. Syst. 48(11), 1851–1862 (2018)

    Google Scholar 

  36. P. Pellanda, P. Apkarian, H. Tuan, Missile autopilot design via a multichannel LFT/LPV control method. Int. J. Robust Nonlinear Control 12(1), 1–20 (2002)

    MATH  Google Scholar 

  37. H. Shen, L. Su, Z.G. Wu, H.P. Ju, Reliable dissipative control for Markov jump systems using an event-triggered sampling information scheme. Nonlinear Anal. Hybrid Syst. 25, 41–59 (2017)

    MathSciNet  MATH  Google Scholar 

  38. P. Shi, Y. Xia, G.P. Liu, D. Rees, On designing of sliding-mode control for stochastic jump systems. IEEE Trans. Autom. Control 51(1), 97–103 (2006)

    MathSciNet  MATH  Google Scholar 

  39. S. Song, J. Hu, D. Chen, W. Chen, Z. Wu, An event-triggered approach to robust fault detection for nonlinear uncertain Markovian jump systems with time-varying delays. Circuits Syst. Signal Process. (2019). https://doi.org/10.1007/s00034-019-01327-3

    Article  MATH  Google Scholar 

  40. Y.X. Su, Q.L. Wang, C.Y. Sun, Self-triggered consensus control for linear multi-agent systems with input saturation. IEEE/CAA J. Autom. Sin. 7(1), 150–157 (2020)

    Google Scholar 

  41. Y. Tan, D. Du, Q. Qi, State estimation for Markovian jump systems with an event-triggered communication scheme. Circuits Syst. Signal Process. 36(1), 1–23 (2016)

    MathSciNet  Google Scholar 

  42. E. Tian, D. Yue, G. Wei, Robust control for Markovian jump systems with partially known transition probabilities and nonlinearities. J. Frankl. Inst. 350(8), 2069–2083 (2013)

    MathSciNet  MATH  Google Scholar 

  43. Z. Wang, Y. Liu, X. Liu, Exponential stabilization of a class of stochastic system with Markovian jump parameters and mode-dependent mixed time-delays. IEEE Trans. Autom. Control 55(7), 1656–1662 (2010)

    MathSciNet  MATH  Google Scholar 

  44. H. Wang, P. Shi, R.K. Agarwal, Network-based event-triggered filtering for Markovian jump systems. Int. J. Control 89(6), 1–23 (2016)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  46. W. Wang, H. Liang, Y. Pan, T. Li, Prescribed performance adaptive fuzzy containment control for nonlinear multi-agent systems using disturbance observer. IEEE Trans. Cybern. (2020). https://doi.org/10.1109/TCYB.2020.2969499

    Article  Google Scholar 

  47. L. Wu, P. Shi, H. Gao, State estimation and sliding-mode control of Markovian jump singular systems. IEEE Trans. Autom. Control 55(5), 1213–1219 (2010)

    MathSciNet  MATH  Google Scholar 

  48. J. Xiong, J. Lam, H. Gao, D.W.C. Ho, On robust stabilization of Markovian jump systems with uncertain switching probabilities. Automatica 41(5), 897–903 (2005)

    MathSciNet  MATH  Google Scholar 

  49. Y. Xu, J.G. Dong, R. Lu, L. Xie, Stability of continuous-time positive switched linear systems: a weak common copositive Lyapunov functions approach. Automatica 97, 278–285 (2018)

    MathSciNet  MATH  Google Scholar 

  50. Y. Xu, Z. Wang, D. Yao, R. Lu, C.Y. Su, State estimation for periodic neural networks with uncertain weight matrices and Markovian jump channel states. IEEE Trans. Syst. Man Cybern. Syst. 48(11), 1841–1850 (2018)

    Google Scholar 

  51. X. Xu, L. Liu, G. Feng, Consensus of single integrator multi-agent systems with unbounded transmission delays. J. Syst. Sci. Complex. 32(3), 778–788 (2019)

    MathSciNet  MATH  Google Scholar 

  52. D. Yao, H. Li, R. Lu, Y. Shi, Distributed sliding mode tracking control of second-order nonlinear multi-agent systems: an event-triggered approach. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2963087

    Article  Google Scholar 

  53. D. Yao, B. Zhang, P. Li, H. Li, Event-triggered sliding mode control of discrete-time Markov jump systems. IEEE Trans. Syst. Man Cybern. Syst. 49(10), 2016–2025 (2019)

    Google Scholar 

  54. D. Yue, E. Tian, Q.L. Han, A delay system method for designing event-triggered controllers of networked control systems. IEEE Trans. Autom. Control 58(2), 475–481 (2013)

    MathSciNet  MATH  Google Scholar 

  55. L. Zhang, H. Liang, H. Ma, Q. Zhou, Fault detection and isolation for semi-Markov jump systems with generally uncertain transition rates based on geometric approach. Circuits Syst. Signal Process. 38, 1039–1062 (2019)

    Google Scholar 

  56. L. Zhang, H. Liang, Y. Sun, C.K. Ahn, Adaptive event-triggered fault detection scheme for semi-Markovian jump systems with output quantization. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2912846

    Article  Google Scholar 

  57. L. Zhang, H.K. Lam, Y. Sun, H. Liang, Fault detection for fuzzy semi-Markov jump systems based on interval type-2 fuzzy approach. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2936333

    Article  Google Scholar 

  58. X.M. Zhang, Q.L. Han, X.H. Ge, D. Ding, L. Ding, D. Yue, C. Peng, Networked control systems: a survey of trends and techniques. IEEE/CAA J. Autom. Sin. 7(1), 1–17 (2020)

    Google Scholar 

  59. Q. Zhou, P. Du, H. Li, R. Lu, J. Yang, Adaptive fixed-time control of error-constrained pure-feedback interconnected nonlinear systems. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2961371

    Article  Google Scholar 

  60. Q. Zhou, W. Wang, H. Ma, H. Li, Event-triggered fuzzy adaptive containment control for nonlinear multi-agent systems with unknown Bouc–Wen hysteresis input. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2961642

    Article  Google Scholar 

  61. Q. Zhou, W. Wang, H. Liang, M. Basin, B. Wang, Observer-based event-triggered Fuzzy adaptive bipartite containment control of multi-agent systems with input quantization. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2953573

    Article  Google Scholar 

  62. W. Zhu, D. Wang, Q. Zhou, Leader-following consensus of multi-agent systems via adaptive event-based control. J. Syst. Sci. Complex. 32(3), 846–856 (2019)

    MathSciNet  MATH  Google Scholar 

  63. Z. Zhu, Y. Pan, Q. Zhou, C. Lu, Event-triggered adaptive fuzzy control for stochastic nonlinear systems with unmeasured states and unknown backlash-like hysteresis. IEEE Trans. Fuzzy Syst. (2020). https://doi.org/10.1109/TFUZZ.2020.2973950

    Article  Google Scholar 

  64. S.Y. Zhu, Y. Liu, Y.J. Lou, J. Cao, Stabilization of logical control networks: an event-triggered control approach. Sci. China Inf. Sci. 63(1), 112203 (2020)

    MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors would like to express our gratitude to the anonymous reviewers for their thoughtful comments and suggestions. This work was partially supported by the National Natural Science Foundation of China (61973091), the Guangdong Natural Science Funds for Distinguished Young Scholar (2017A030306014), the Local Innovative and Research Teams Project of Guangdong Special Support Program of 2019, the Innovative Research Team Program of Guangdong Province Science Foundation (2018B030312006), and the Science and Technology Program of Guangzhou (201904020006).

Author information

Authors and Affiliations

  1. School of Automation and the Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangdong University of Technology, Guangzhou, 510006, China

    Lin Chen, Xiaomeng Li, Wenshuai Lin & Qi Zhou

Authors
  1. Lin Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaomeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wenshuai Lin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qi Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qi Zhou.

Ethics declarations

Conflict of interest

The authors declare that there is 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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, L., Li, X., Lin, W. et al. Adaptive Event-Triggered \(H_{\infty }\) Control for Markov Jump Systems with Generally Uncertain Transition Rates. Circuits Syst Signal Process 39, 5429–5453 (2020). https://doi.org/10.1007/s00034-020-01435-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-020-01435-5

Keywords

Search

Navigation