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Adaptive Observer Design for Quasi-one-sided Lipschitz Nonlinear Systems

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Proceedings of 2017 Chinese Intelligent Systems Conference (CISC 2017)

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Abstract

This paper deals with the adaptive observer design problem for quasi-one-sided Lipschitz nonlinear systems. First, some useful assumptions are presented for the observer design purpose. Then, under the assumptions, an adaptive observer is constructed for the nonlinear system. Finally, a numerical example is given to illustrate the effectiveness of the proposed method.

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References

  1. Krener A, Respondek W. Nonlinear observer with linearizable error dynamics. SIAM J Control Optim. 1985;23(2):197–216.

    Article  MathSciNet  MATH  Google Scholar 

  2. Arcak M, Kokotovic P. Nonlinear observers: a circle criterion design and robustness analysis. Automatica. 2001;37(12):1923–30.

    Article  MathSciNet  MATH  Google Scholar 

  3. Ibrir S. Circle-criterion approach to discrete-time nonlinear observer design. Automatica. 2007;43(8):1432–41.

    Article  MathSciNet  MATH  Google Scholar 

  4. Starkov K, Coria L, Aguilar L. On synchronization of chaotic systems based on the Thau observer design. Commun Nonlinear Sci Numer Simul. 2012;17(1):17–25.

    Article  MathSciNet  MATH  Google Scholar 

  5. Huang J, Han Z, Cai X, Liu L. Adaptive full-order and reduced-order observers for the Lur’e differential inclusion system. Commun Nonlinear Sci Numer Simul. 2011;16(7):2869–79.

    Article  MathSciNet  MATH  Google Scholar 

  6. Huang J, Han Z. Adaptive non-fragile observer design for the uncertain Lur’e differential inclusion system. Appl Math Model. 2013;37(1–2):72–81.

    Article  MathSciNet  MATH  Google Scholar 

  7. Pertew A, Marquez H, Zhao Q. \(H_{\infty }\) observer design for Lipschitz nonlinear systems. IEEE Trans Autom Control. 2006;51(7):1211–6.

    Article  MathSciNet  MATH  Google Scholar 

  8. Zhang W, Su H, Su S, Wang D. Nonlinear \(H_{\infty }\) observer design for one-sided Lipschitz systems. Neurocomputing. 2014;145:505–11.

    Article  Google Scholar 

  9. Zheng G, Efimov D, Bejarano F, Perruquetti W, Wang H. Interval observer for a class of uncertain nonlinear singular systems. Automatica. 2016;71:159–68.

    Article  MathSciNet  MATH  Google Scholar 

  10. He Z, Xie W. Control of non-linear switched systems with average dwell time: interval observer-based framework. IET Control Theory Appl. 2016;10(1):10–6.

    Article  MathSciNet  Google Scholar 

  11. Zhang W, Su H, Liang Y, Han Z. Non-linear observer design for one-sided Lipschitz systems: an linear matrix inequality approach. IET Control Theory Appl. 2012;6(9):1297–303.

    Article  MathSciNet  Google Scholar 

  12. Zhang W, Su H, Wang H, Han Z. Full-order and reduced-order observers for one-sided Lipschitz nonlinear systems using Riccati equations. Commun Nonlinear Sci Numer Simul. 2012;17(12):4968–77.

    Article  MathSciNet  MATH  Google Scholar 

  13. Osorio M, Moreno J. Dissipative design of observers for multivalued nonlinear systems. In: Proceedings of the 45th IEEE conference on decision and control. 2006.

    Google Scholar 

  14. Doris A, Juloski A, Mihajlovic N, Heemels W, Wouw N, Nijmeijer H. Observer designs for experimental non-smooth and discontinuous systems. IEEE Trans Control Syst Technol. 2008;16(6):1323–32.

    Article  Google Scholar 

  15. Brogliato B, Heemels W. Observer design for Lur’e systems with multivalued mappings: a passivity approach. IEEE Trans Autom Control. 2009;54(8):1996–2001.

    Article  MATH  Google Scholar 

  16. Hu G. Observers for one-sided Lipschitz non-linear systems. IMA J Math Control Inf. 2006;23(4):395–401.

    Article  MathSciNet  MATH  Google Scholar 

  17. Hu G. A note on observer for one-sided Lipschitz non-linear systems. IMA J Math Control Inf. 2008;25(3):297–303.

    Article  MathSciNet  MATH  Google Scholar 

  18. Abbaszadeh M, Marquez H. Nonlinear observer design for one-sided Lipschitz systems. In: Proceedings of the American control conference. 2010.

    Google Scholar 

  19. Zhao Y, Tao J, Shi N. A note on observer design for one-sided Lipschitz nonlinear systems. Syst Control Lett. 2010;59(1):66–71.

    Article  MathSciNet  MATH  Google Scholar 

  20. Chen Z, He Y, Wu M. Robust stabilization of nonlinear networked control systems with quasi-one-sided Lipschitz condition. In: Proceedings of the 2010 IEEE international conference on mechatronics and automation. 2010.

    Google Scholar 

  21. Fu F, Hou M, Duan G. Stabilization of quasi-one-sided Lipschitz nonlinear systems. IMA J Math Control Inf. 2013;30(2):169–84.

    Article  MathSciNet  MATH  Google Scholar 

  22. Li L, Yang Y, Zhang Y, Ding S. Fault estimation of one-sided Lipschitz and quasi-one-sided Lipschitz systems. In: Proceedings of the 33rd Chinese control conference. 2014.

    Google Scholar 

  23. Song J, He S. Finite-time \(H_{\infty }\) control for quasi-one-sided Lipschitz nonlinear systems. Neurocomputing. 2015;149(Part C):1433–9.

    Google Scholar 

  24. Kristic M, Modestino J, Deng H. Stabilization of nonlinear uncertain systems. New York: Springer; 1998.

    Google Scholar 

  25. Zhang W, Su H, Zhu F, Bhattacharyya S. Improved exponential observer design for one-sided Lipschitz nonlinear systems. Int J Robust Nonlinear Control. 2016;26(18):3958–73.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are grateful for the National Natural Science Foundation of China (61403267, 61403268), Natural Science Foundation of Jiangsu Province of China (BK20130322), and China Postdoctoral Science Foundation (2017M611903).

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Correspondence to Jun Huang .

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Huang, J., Yu, L., Shi, M. (2018). Adaptive Observer Design for Quasi-one-sided Lipschitz Nonlinear Systems. In: Jia, Y., Du, J., Zhang, W. (eds) Proceedings of 2017 Chinese Intelligent Systems Conference. CISC 2017. Lecture Notes in Electrical Engineering, vol 459. Springer, Singapore. https://doi.org/10.1007/978-981-10-6496-8_2

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  • DOI: https://doi.org/10.1007/978-981-10-6496-8_2

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  • Print ISBN: 978-981-10-6495-1

  • Online ISBN: 978-981-10-6496-8

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