Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Global practical tracking for stochastic time-delay nonlinear systems with SISS-like inverse dynamics

Abstract

This paper investigates the practical tracking problem of stochastic delayed nonlinear systems. The powers of the nonlinear terms are relaxed to a certain interval rather than a precisely known point. Based on the Lyapunov-Krasovskii (L-K) functional method and the modified adding a power integrator technique, a new controller is constructed to render the solutions of the considered system to be bounded in probability, and furthermore, the tracking error in sense of the mean square can be made small enough by adjusting some designed parameters. A simulation example is provided to demonstrate the validity of the method in this paper.

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

References

  1. 1

    Zhang W H, Chen B S. On stabilizability and exact observability of stochastic systems with their applications. Automatica, 2004, 40: 87–94

  2. 2

    Zhang W H, Zhang H S, Chen B S. Generalized Lyapunov equation approach to state-dependent stochastic stabilization/ detectability criterion. IEEE Trans Automat Contr, 2008, 53: 1630–1642

  3. 3

    Xie X J, Duan N, Yu X. State-feedback control of high-order stochastic nonlinear systems with SiISS inverse dynamics. IEEE Trans Automat Contr, 2011, 56: 1921–1926

  4. 4

    Zhao X Y, Deng F Q. Divided state feedback control of stochastic systems. IEEE Trans Automat Contr, 2015, 60: 1870–1885

  5. 5

    Yu X, Xie X J. Output feedback regulation of stochastic nonlinear systems with stochastic iISS inverse dynamics. IEEE Trans Automat Contr, 2010, 55: 304–320

  6. 6

    Wu M, He Y, She J H, et al. Delay-dependent criteria for robust stability of time-varying delay systems. Automatica, 2004, 40: 1435–1439

  7. 7

    Zhou G P, Huang J H, Tian F X, et al. Sufficient and necessary conditions for global stability of genetic regulator networks with time delays. Sci China Inf Sci, 2016, 59: 012202

  8. 8

    Liu Z W, Zhang H G, Sun Q Y. Static output feedback stabilization for systems with time-varying delay based on a matrix transformation method. Sci China Inf Sci, 2015, 58: 012201

  9. 9

    Yan X H, Liu Y G. Global practical tracking by output-feedback for nonlinear systems with unknown growth rate. Sci China Inf Sci, 2011, 54: 2079–2090

  10. 10

    Li W Q, Wu Z J. Output tracking of stochastic high-order nonlinear systems with Markovian switching. IEEE Trans Automat Contr, 2013, 58: 1585–1590

  11. 11

    Li W Q, Zhang J F. Distributed practical output tracking of high-order stochastic multi-agent systems with inherent nonlinear drift and diffusion terms. Automatica, 2014, 50: 3231–3238

  12. 12

    Li W Q, Liu L, Feng G. Distributed containment tracking of multiple stochastic nonlinear system. Automatica, 2016, 69: 214–221

  13. 13

    Wu Z J, Yang J, Shi P. Adaptive tracking for stochastic nonlinear systems with Markovian switching. IEEE Trans Automat Contr, 2010, 55: 2135–2141

  14. 14

    Wu Z J, Cui M Y, Shi P. Vector backstepping control for stochastic Hamiltonian systems. SIAM J Control Optim, 2012, 50: 925–942

  15. 15

    Xie X J, Zhao C R, Duan N. Further results on state feedback stabilization of stochastic high-order nonlinear systems. Sci China Inf Sci, 2014, 57: 072202

  16. 16

    Zhang K M, Zhao C R, Xie X J. Global output feedback stabilisation of stochastic high-order feedforward nonlinear systems with time delay. Int J Contr, 2015, 88: 2477–2487

  17. 17

    Zhang W H, Chen B S. State feedback H8 control for a class of nonlinear stochastic systems. SIAM J Control Optim, 2006, 44: 1973–1991

  18. 18

    Hu Z P, Deng F Q. Robust H8 control for networked systems with transmission delays and successive packet dropouts under stochastic sampling. Int J Robust Nonlinear Contr, 2017, 27: 84–107

  19. 19

    Xie X J, Duan N. Output tracking of high-order stochastic nonlinear systems with application to benchmark mechanical system. IEEE Trans Automat Contr, 2010, 55: 1197–1202

  20. 20

    Jin S L, Liu Y G. Global practical tracking via adaptive output-feedback for uncertain nonlinear systems with generalized control coefficients. Sci China Inf Sci, 2016, 59: 012203

  21. 21

    Xue L R, Zhang W H, Lin Y N. Global output tracking control for high-order stochastic nonlinear systems with SISS inverse dynamics and time-varying delays. J Franklin Inst, 2016, 353: 3249–3270

  22. 22

    Sun Z Y, Liu Z G, Zhang X H. New results on global stabilization for time delay nonlinear systems with low-order and high-order growth conditions. Int J Robust Nonlinear Contr, 2015, 25: 878–899

  23. 23

    Liu S J, Zhang J F, Jiang Z P. Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems. Automatica, 2007, 43: 238–251

  24. 24

    Liu S J, Ge S S, Zhang J F. Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays. Int J Contr, 2008, 81: 1210–1220

  25. 25

    Sun Z Y, Xue L R, Zhang K M. A new approach to finite-time adaptive stabilization of high-order uncertain nonlinear system. Automatica, 2015, 58: 60–66

  26. 26

    Mao X R. Stochastic Differential Equations and Applications. North-Holland: Elsevier, 2007

  27. 27

    Mao X R. A note on the LaSalle-type theorems for stochastic differential delay equations. Appl Math Comput, 2002, 268: 125–142

  28. 28

    Khalil H K, Grizzle J W. Nonlinear Systems. 3rd ed. New Jersey: Prentice Hall, 1996. 144–145

  29. 29

    Wu Y Q, Liu Z G. Output feedback stabilization for time-delay nonholonomic systems with polynomial conditions. ISA Trans, 2015, 58: 1–10

Download references

Acknowledgments

This work was supported by National Natural Science Foundation of China (Grant Nos. 61573227, 61633014, 61673242, 61603231), State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (Grant No. LAPS16011), Research Fund for the Taishan Scholar Project of Shandong Province of China, Postgraduate Innovation Funds of SDUST (No. SDKDYC170229), SDUST Research Fund (Grant No. 2015TDJH105), and Shandong Provincial Natural Science Foundation of China (Grant No. 2016ZRB01076).

Author information

Correspondence to Weihai Zhang.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Xue, L., Zhang, W. & Xie, X. Global practical tracking for stochastic time-delay nonlinear systems with SISS-like inverse dynamics. Sci. China Inf. Sci. 60, 122201 (2017). https://doi.org/10.1007/s11432-016-0448-2

Download citation

Keywords

  • nonlinear systems
  • stochastic systems
  • time-varying delay
  • global practical tracking
  • SISS-like inverse dynamics