SpringerLink
Log in

Output feedback stabilization of stochastic high-order planar nonlinear systems with stochastic inverse dynamics and output-constraint

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

In this paper, we solve the output feedback control problem of stochastic high-order planar nonlinear systems with output constraint and stochastic integral input-to-state stability (SiISS) inverse dynamics. By employing a key coordinate transformation, a stochastic nonlinear system with output constraint and SiISS inverse dynamics is converted into an unconstrained system. By skillfully constructing an observer and adopting SiISS small-gain conditions, we develop a new output feedback control design and analysis method, and prove that all the closed-system signals are bounded almost surely, the output constraint is not violated almost surely, and the equilibrium point of the closed-loop system is stochastically asymptotically stable.

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
EUR 32.99 /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

Similar content being viewed by others

References

  1. Lin W, Qian C J. Adding one power integrator: a tool for global stabilization of high-order lower-triangular systems. Syst Control Lett, 2000, 39: 339–351

    Article  MathSciNet  Google Scholar 

  2. **e X J, Tian J. Adaptive state-feedback stabilization of high-order stochastic systems with nonlinear parameterization. Automatica, 2009, 45: 126–133

    Article  MathSciNet  Google Scholar 

  3. Li W Q, **e X J. Inverse optimal stabilization for stochastic nonlinear systems whose linearizations are not stabilizable. Automatica, 2009, 45: 498–503

    Article  MathSciNet  Google Scholar 

  4. Li W Q, **g Y W, Zhang S Y. Adaptive state-feedback stabilization for a large class of high-order stochastic nonlinear systems. Automatica, 2011, 47: 819–828

    Article  MathSciNet  Google Scholar 

  5. Li W Q, Liu X H, Zhang S Y. Further results on adaptive state-feedback stabilization for stochastic high-order nonlinear systems. Automatica, 2012, 48: 1667–1675

    Article  MathSciNet  Google Scholar 

  6. **e X J, Liu L. A homogeneous domination approach to state feedback of stochastic high-order nonlinear systems with time-varying delay. IEEE Trans Automat Contr, 2013, 58: 494–499

    Article  MathSciNet  Google Scholar 

  7. Zhao C R, **e X J. Global stabilization of stochastic high-order feedforward nonlinear systems with time-varying delay. Automatica, 2014, 50: 203–210

    Article  MathSciNet  Google Scholar 

  8. Xue L R, Zhang T L, Zhang W H, et al. Global adaptive stabilization and tracking control for high-order stochastic nonlinear systems with time-varying delays. IEEE Trans Automat Contr, 2018, 63: 2928–2943

    Article  MathSciNet  Google Scholar 

  9. Niu B, Liu M, Li A. Global adaptive stabilization of stochastic high-order switched nonlinear non-lower triangular systems. Syst Control Lett, 2020, 136: 104596

    Article  MathSciNet  Google Scholar 

  10. **e X J, Li W Q. Output-feedback control of a class of high-order stochastic nonlinear systems. Int J Control, 2009, 82: 1692–1705

    Article  MathSciNet  Google Scholar 

  11. Li W Q, **g Y W, Zhang S Y. Output-feedback stabilization for stochastic nonlinear systems whose linearizations are not stabilizable. Automatica, 2010, 46: 752–760

    Article  MathSciNet  Google Scholar 

  12. Li W Q, **e X J, Zhang S Y. Output-feedback stabilization of stochastic high-order nonlinear systems under weaker conditions. SIAM J Control Optim, 2011, 49: 1262–1282

    Article  MathSciNet  Google Scholar 

  13. **e 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

    Article  MathSciNet  Google Scholar 

  14. **e X J, Duan N, Zhao C R. A combined homogeneous domination and sign function approach to output-feedback stabilization of stochastic high-order nonlinear systems. IEEE Trans Automat Contr, 2014, 59: 1303–1309

    Article  MathSciNet  Google Scholar 

  15. Tee K P, Ge S S, Tay E H. Barrier Lyapunov functions for the control of output-constrained nonlinear systems. Automatica, 2009, 45: 918–927

    Article  MathSciNet  Google Scholar 

  16. Fang L D, Ma L, Ding S H, et al. Finite-time stabilization for a class of high-order stochastic nonlinear systems with an output constraint. Appl Math Computation, 2019, 358: 63–79

    Article  MathSciNet  Google Scholar 

  17. Fang L D, Ma L, Ding S H, et al. Finite-time stabilization of high-order stochastic nonlinear systems with asymmetric output constraints. IEEE Trans Syst Man Cybern Syst, 2021, 51: 7201–7213

    Article  Google Scholar 

  18. Fang L D, Ding S H, Park J H, et al. Adaptive fuzzy control for nontriangular stochastic high-order nonlinear systems subject to asymmetric output constraints. IEEE Trans Cybern, 2022, 52: 1280–1291

    Article  PubMed  Google Scholar 

  19. Cui R H, **e X J. Adaptive state-feedback stabilization of state-constrained stochastic high-order nonlinear systems. Sci China Inf Sci, 2021, 64: 200203

    Article  MathSciNet  Google Scholar 

  20. Fang L D, Ding S H, Park J H, et al. Adaptive fuzzy output-feedback control design for a class of p-norm stochastic nonlinear systems with output constraints. IEEE Trans Circuits Syst I, 2021, 68: 2626–2638

    Article  MathSciNet  Google Scholar 

  21. Fang L D, Ma L, Ding S H. Finite-time fuzzy output-feedback control for p-norm stochastic nonlinear systems with output constraints. AIMS Mathematics, 2021, 6: 2244–2267

    Article  MathSciNet  Google Scholar 

  22. Cui R H, **e X J. Output feedback stabilization of stochastic planar nonlinear systems with output constraint. Automatica, 2022, 143: 110471

    Article  MathSciNet  Google Scholar 

  23. Bechlioulis C P, Rovithakis G A. Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance. IEEE Trans Automat Contr, 2008, 53: 2090–2099

    Article  MathSciNet  Google Scholar 

  24. Sontag E D. Smooth stabilization implies coprime factorization. IEEE Trans Automat Contr, 1989, 34: 435–443

    Article  MathSciNet  Google Scholar 

  25. Sontag E D. Comments on integral variants of ISS. Syst Control Lett, 1998, 34: 93–100

    Article  MathSciNet  Google Scholar 

  26. Tsinias J. Stochastic input-to-state stability and applications to global feedback stabilization. Int J Control, 1998, 71: 907–930

    Article  MathSciNet  Google Scholar 

  27. Tang C, Basar T. Stochastic stability of singularly perturbed nonlinear systems. In: Proceedings of the 40th IEEE Conference on Decision and Control, 2001. 399–404

  28. 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

    Article  MathSciNet  Google Scholar 

  29. **e X J, Tian J. State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics. Intl J Robust Nonlinear, 2007, 17: 1343–1362

    Article  MathSciNet  Google Scholar 

  30. Xue L R, Zhang W H, **e X J. Global practical tracking for stochastic time-delay nonlinear systems with SISS-like inverse dynamics. Sci China Inf Sci, 2017, 60: 122201

    Article  MathSciNet  Google Scholar 

  31. Zhao C R, **e X J. Output feedback stabilization using small-gain method and reduced-order observer for stochastic nonlinear systems. IEEE Trans Automat Contr, 2013, 58: 523–529

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  33. Yu X, **e X J, Duan N. Small-gain control method for stochastic nonlinear systems with stochastic iISS inverse dynamics. Automatica, 2010, 46: 1790–1798

    Article  MathSciNet  Google Scholar 

  34. Duan N, **e X J, Yu X. State feedback stabilization of stochastic nonlinear systems with SiISS inverse dynamics. Intl J Robust Nonlinear, 2011, 21: 1903–1919

    Article  MathSciNet  Google Scholar 

  35. **e 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

    Article  MathSciNet  Google Scholar 

  36. Yu X, **e X J, Wu Y Q. Further results on output-feedback regulation of stochastic nonlinear systems with SiISS inverse dynamics. Int J Control, 2010, 83: 2140–2152

    Article  MathSciNet  Google Scholar 

  37. Duan N, Yu X, **e X J. Output feedback control using small-gain conditions for stochastic nonlinear systems with SiISS inverse dynamics. Int J Control, 2011, 84: 47–56

    Article  MathSciNet  Google Scholar 

  38. Deng H, Krstic M, Williams R J. Stabilization of stochastic nonlinear systems driven by noise of unknown covariance. IEEE Trans Automat Contr, 2001, 46: 1237–1253

    Article  MathSciNet  Google Scholar 

  39. Qian C J, Lin W. Non-Lipschitz continuous stabilizers for nonlinear systems with uncontrollable unstable linearization. Syst Control Lett, 2001, 42: 185–200

    Article  MathSciNet  Google Scholar 

  40. Lin W, Qian C J. Adaptive control of nonlinearly parameterized systems: the smooth feedback case. IEEE Trans Automat Contr, 2002, 47: 1249–1266

    Article  MathSciNet  Google Scholar 

  41. Sun Z Y, Zhang X H, **e X J. Global continuous output-feedback stabilization for a class of high-order nonlinear systems with multiple time delays. J Franklin Institute, 2014, 351: 4334–4356

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 62221004, 62073166).

Author information

Authors and Affiliations

  1. School of Automation, Nan**g University of Science and Technology, Nan**g, 210094, China

    Ruiming **e & Shengyuan Xu

Authors
  1. Ruiming **e
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shengyuan Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shengyuan Xu.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

**e, R., Xu, S. Output feedback stabilization of stochastic high-order planar nonlinear systems with stochastic inverse dynamics and output-constraint. Sci. China Inf. Sci. 67, 132205 (2024). https://doi.org/10.1007/s11432-023-3875-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-023-3875-5

Keywords

Search

Navigation