Skip to main content
SpringerLink
Log in

Adaptive State Observers for Incrementally Quadratic Nonlinear Systems with Application to Chaos Synchronization

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

Abstract

This paper is concerned with the problem of adaptive state observer design for a class of incrementally quadratic nonlinear systems with parameter uncertainty. Its nonlinearity satisfies the condition of incremental quadratic constraints which contains many commonly encountered nonlinearities in existing literature as some special cases. A circle criterion-based adaptive observer is first designed to expand the freedom of observer design. Based on the incremental quadratic constraint condition, sufficient conditions ensuring asymptotic stability of estimation error dynamics are established in terms of linear matrix inequalities. Finally, the adaptive observer is applied to the synchronization design of chaotic systems with parameter uncertainty, which fully demonstrates the effectiveness of the proposed observer.

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

Similar content being viewed by others

References

  1. M. Abbaszadeh, H.J. Marquez, Nonlinear observer design for one-sided Lipschitz systems, in Proceedings of the 2010 American Control Conference, pp. 5284–5289 (2010)

  2. B. Açıkmeşe, M. Corless, Observers for systems with nonlinearities satisfying incremental quadratic constraints. Automatica 47(7), 1339–1348 (2011)

    Article  MathSciNet  Google Scholar 

  3. I. Ahmad, M. Shafiq, M. Shahzad, Global finite-time multi-switching synchronization of externally perturbed chaotic oscillators. Circuits Syst. Signal Process. 37(12), 5253–5278 (2018)

    Article  MathSciNet  Google Scholar 

  4. M. Arcak, P. Kokotovic, Observer-based control of systems with slope-restricted nonlinearities. IEEE Trans. Autom. Control 46(7), 1146–1150 (2001)

    Article  MathSciNet  Google Scholar 

  5. M. Ayati, H. Khaloozadeh, A stable adaptive synchronization scheme for uncertain chaotic systems via observer. Chaos Soliton. Fract. 42(4), 2473–2483 (2009)

    Article  MathSciNet  Google Scholar 

  6. A. Barbata, M. Zasadzinski, H.S. Ali, H. Messaoud, Exponential observer for a class of one-sided Lipschitz stochastic nonlinear systems. IEEE Trans. Autom. Control 60(1), 259–264 (2015)

    Article  MathSciNet  Google Scholar 

  7. M. Benallouch, M. Boutayeb, M. Zasadzinski, Observer design for one-sided Lipschitz discrete-time systems. Syst. Control Lett. 61(9), 879–886 (2012)

    Article  MathSciNet  Google Scholar 

  8. S. Bowong, J.J. Tewa, Unknown inputs adaptive observer for a class of chaotic systems with uncertainties. Math. Comput. Model. 48(11), 1826–1839 (2008)

    Article  MathSciNet  Google Scholar 

  9. S. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory (SIAM, Philadelphia, 1994)

    Book  Google Scholar 

  10. L. Cao, H. Li, N. Wang, Q. Zhou, Observer-based event-triggered adaptive decentralized fuzzy control for nonlinear large-scale systems. IEEE Trans. Fuzzy Syst. 27(6), 1201–1214 (2018)

    Article  Google Scholar 

  11. L. Cao, Q. Zhou, G. Dong, Observer-based adaptive event-triggered control for nonstrict-feedback nonlinear systems with output constraint and actuator failures. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2019.2895858

  12. A. Chakrabarty, M.J. Corless, G.T. Buzzard, S.H. Żak, A.E. Rundell, State and unknown input observers for nonlinear systems with bounded exogenous inputs. IEEE Trans. Autom. Control 62(11), 5497–5510 (2017)

    Article  MathSciNet  Google Scholar 

  13. Y. Cho, R. Rajamani, A systematic approach to adaptive observer synthesis for nonlinear systems. IEEE Trans. Autom. Control 42(4), 534–537 (1997)

    Article  MathSciNet  Google Scholar 

  14. L. D’Alto, M. Corless, Incremental quadratic stability. Numer. Algebra Control Optim. 3(1), 175–201 (2013)

    Article  MathSciNet  Google Scholar 

  15. H. Dimassi, A. Loria, Adaptive unknown-input observers-based synchronization of chaotic systems for telecommunication. IEEE Trans. Circuits Syst. I, Reg. Papers 58(4), 800–812 (2011)

    Article  MathSciNet  Google Scholar 

  16. H. Dimassi, A. Loría, S. Belghith, A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers. Commun. Nonlinear Sci. Numer. Simulat. 17(9), 3727–3739 (2012)

    Article  Google Scholar 

  17. M. Ekramian, F. Sheikholeslam, S. Hosseinnia, M.J. Yazdanpanah, Adaptive state observer for Lipschitz nonlinear systems. Syst. Control Lett. 62(4), 319–323 (2013)

    Article  MathSciNet  Google Scholar 

  18. H. Li, Y. Gao, P. Shi, H.K. Lam, Observer-based fault detection for nonlinear systems with sensor fault and limited communication capacity. IEEE Trans. Autom. Control 61(9), 2745–2751 (2016)

    Article  MathSciNet  Google Scholar 

  19. X. Li, D. Ho, J. Cao, Finite-time stability and settling-time estimation of nonlinear impulsive systems. Automatica 99, 361–368 (2019)

    Article  MathSciNet  Google Scholar 

  20. W. Li, Z. Liu, J. Miao, Adaptive synchronization for a unified chaotic system with uncertainty. Commun. Nonlinear Sci. Numer. Simulat. 15(10), 3015–3021 (2010)

    Article  Google Scholar 

  21. X. Li, J. Wu, Stability of nonlinear differential systems with state-dependent delayed impulses. Automatica 64, 63–69 (2016)

    Article  MathSciNet  Google Scholar 

  22. X. Li, J. Wu, Sufficient stability conditions of nonlinear differential systems under impulsive control with state-dependent delay. IEEE Trans. Autom. Control 63(1), 306–311 (2018)

    Article  MathSciNet  Google Scholar 

  23. H. Liang, Z. Zhang, C. K. Ahn, Event-triggered fault detection and isolation of discrete-time systems based on geometric technique. IEEE Trans. Circuits Syst. II, Exp. Briefs (2019). https://doi.org/10.1109/TCSII.2019.2912846

  24. H. Liang, Y. Zhang, T. Huang, H. Ma, Prescribed performance cooperative control for multiagent systems with input quantization. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2893645

  25. H. Ma, H. Li, H. Liang, G. Dong, Adaptive fuzzy event-triggered control for stochastic nonlinear systems with full state constraints and actuator faults. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2896843

    Article  Google Scholar 

  26. L. Pecora, T. Carroll, Synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)

    Article  MathSciNet  Google Scholar 

  27. M. Pourgholi, V.J. Majd, A nonlinear adaptive resilient observer design for a class of Lipschitz systems using LMI. Circuits Syst. Signal Process. 30(6), 1401–1415 (2011)

    Article  MathSciNet  Google Scholar 

  28. R. Rajamani, Observers for Lipschitz nonlinear systems. IEEE Trans. Autom. Control 43(3), 397–401 (1998)

    Article  MathSciNet  Google Scholar 

  29. H. Su, H. Wu, X. Chen, Observer-based discrete-time nonnegative edge synchronization of networked systems. IEEE Trans. Neural Netw. Learn. Syst. 28(10), 2446–2455 (2017)

    Article  MathSciNet  Google Scholar 

  30. H. Su, H. Wu, X. Chen, M.Z.Q. Chen, Positive edge consensus of complex networks. IEEE Trans. Syst. Man Cybern. Syst. 48(12), 2242–2250 (2018)

    Article  Google Scholar 

  31. H. Su, H. Wu, J. Lam, Positive edge-consensus for nodal networks via output feedback. IEEE Trans. Autom. Control 64(3), 1244–1249 (2019)

    Article  MathSciNet  Google Scholar 

  32. G. Tao, A simple alternative to the Barbalat lemma. IEEE Trans. Autom. Control 42(5), 698 (1997)

    Article  MathSciNet  Google Scholar 

  33. S.J. Theesar, P. Balasubramanian, Secure communication via synchronization of Lure systems using sampled-data controller. Circuits Syst. Signal Process. 33(1), 37–52 (2014)

    Article  Google Scholar 

  34. E. Wu, X. Yang, Generalized lag synchronization of neural networks with discontinuous activations and bounded perturbations. Circuits Syst. Signal Process. 34(7), 2381–2394 (2015)

    Article  MathSciNet  Google Scholar 

  35. R. Wu, W. Zhang, F. Song, Z. Wu, W. Guo, Observer-based stabilization of one-sided Lipschitz systems with application to flexile link manipulator. Adv. Mech. Eng. 7(12), 1–8 (2015)

    Article  Google Scholar 

  36. A. Zemouche, M. Boutayeb, A unified \(H_\infty \) adaptive observer synthesis method for a class of systems with both Lipschitz and monotone nonlinearities. Syst. Control Lett. 58(4), 282–28 (2009)

    Article  MathSciNet  Google Scholar 

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

  38. Z. Zhang, H. Liang, C. Wu, C.K. Ahn, Adaptive event-triggered output feedback fuzzy control for nonlinear networked systems with packet dropouts and random actuator failure. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2891236

    Article  Google Scholar 

  39. W. Zhang, H. Su, H. Wang, Z. Han, Full-order and reduced-order observers for one-sided Lipschitz nonlinear systems using Riccati equations. Commun. Nonlinear Sci. Numer. Simulat. 17(12), 4968–4977 (2012)

    Article  MathSciNet  Google Scholar 

  40. W. Zhang, H. Su, F. Zhu, G.M. Azar, Unknown input observer design for one-sided Lipschitz nonlinear systems. Nonlinear Dyn. 79(2), 1469–1479 (2015)

    Article  MathSciNet  Google Scholar 

  41. W. Zhang, H. Su, F. Zhu, M. Wang, Observer-based \(H_{\infty }\) synchronization and unknown input recovery for a class of digital nonlinear systems. Circuits Syst. Signal Process. 32, 2867–2881 (2013)

    Article  MathSciNet  Google Scholar 

  42. W. Zhang, H. Su, F. Zhu, D. Yue, A note on observers for discrete-time Lipschitz nonlinear systems. IEEE Trans. Circuits Syst. II, Exp. Briefs 59(2), 123–127 (2012)

    Article  Google Scholar 

  43. W. Zhang, Y. Zhao, M. Abbaszadeh, M. Ji, Full-order and reduced-order exponential observers for discrete-time nonlinear systems with incremental quadratic constraints. J. Dyn. Syst. Meas. Control 141, 041005-1-9 (2019)

    Google Scholar 

  44. Y. Zhao, W. Zhang, H. Su, J. Yang, Observer-based synchronization of chaotic systems satisfying incremental quadratic constraints and its application in secure communication. IEEE Trans. Syst. Man Cybern. Syst. (2019). https://doi.org/10.1109/TSMC.2018.2868482

  45. Y. Zhao, W. Zhang, W. Zhang, F. Song, Exponential reduced-order observers for nonlinear systems satisfying incremental quadratic constraints. Circuits Syst. Signal Process. 37(9), 3725–3738 (2018)

    Article  MathSciNet  Google Scholar 

  46. F. Zhu, Z. Han, A note on observers for Lipschitz nonlinear systems. IEEE Trans. Autom. Control 47(10), 1751–1754 (2002)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grant No. 61603241 and the Project of Science and Technology Commission of Shanghai Municipality under Grant No. 17030501400.

Author information

Authors and Affiliations

  1. Laboratory of Intelligent Control and Robotics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Hongzhi Zhang, Wei Zhang, Younan Zhao & Mingming Ji

  2. School of Information Technology and Mechanical and Electrical Integration, Shanghai Zhongqiao College, Shanghai, 201310, China

    Lixin Huang

Authors
  1. Hongzhi Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wei Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Younan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mingming Ji
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lixin Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wei Zhang.

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

Zhang, H., Zhang, W., Zhao, Y. et al. Adaptive State Observers for Incrementally Quadratic Nonlinear Systems with Application to Chaos Synchronization. Circuits Syst Signal Process 39, 1290–1306 (2020). https://doi.org/10.1007/s00034-019-01207-w

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00034-019-01207-w

Keywords

Search

Navigation