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Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs - application to chaos synchronization

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This work addresses the problem of adaptive observer design for nonlinear systems satisfying incremental quadratic constraints. The output of the system includes nonlinear terms, which puts an additional strain on the design and feasibility of the observer, which is guaranteed under the satisfaction of an LMI, and a set of algebraic constraints. A particular case where the output nonlinearity matches the unknown parameter coefficient is also discussed. The result is illustrated through a numerical example for the chaos synchronization of the Rössler system.
Rocznik
Strony
105--121
Opis fizyczny
Bibliogr. 31 poz., rys., wzory
Twórcy
  • Laboratory of Nonlinear Systems - Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece
  • Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur, India
  • Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur, India
  • Department of Mathematics, Zhejiang Normal University, Jinhua, China
  • Laboratory of Nonlinear Systems - Circuits & Complexity, Physics Department, Aristotle University of Thessaloniki, Thessaloniki, Greece
Bibliografia
  • [1] R. Rajamani: Observers for Lipschitz nonlinear systems. IEEE transactions on Automatic Control, 43(3), (1998), 397-401. DOI: 10.1109/9.661604.
  • [2] M. Kumar Gupta, N, Kumar Tomar and S. Bhaumik: Full- and reduced-order observer design for rectangular descriptor systems with unknown inputs. Journal of the Franklin Institute, 352(3), (2015), 1250-1264. DOI: 10.1016/j.jfranklin.2015.01.003.
  • [3] M. Kumar Gupta, N. Kumar Tomar, V. Kumar Mishra and S. Bhaumik: Observer design for semilinear descriptor systems with applications to chaos-based secure communication. International Journal of Applied and Computational Mathematics, 3(1), (2017), 1313-1324. DOI: 10.1007/s40819-017-0419-0.
  • [4] Ch. Hua, X. Guan, X. Li and P. Shi; Adaptive observer-based control for a class of chaotic systems. Chaos, Solitons & Fractals, 22(1), (2004), 103-110. DOI: 10.1016/j.chaos.2003.12.072.
  • [5] R. Carroll and D. Lindorff: An adaptive observer for single-input single-output linear systems. IEEE Transactions on Automatic Control, 18(5), (1973), 428-435. DOI: 10.1109/TAC.1973.1100367.
  • [6] Y. Man Cho and R. Rajamani: A systematic approach to adaptive observer synthesis for nonlinear systems. IEEE Transactions on Automatic Control, 42(4), (1997), 534-537. DOI: 10.1109/9.566664.
  • [7] S. Bowong and J-J. Tewa: Unknown inputs adaptive observer for a class of chaotic systems with uncertainties. Mathematical and Computer Modelling, 48(11-12), (2008), 1826 1839. DOI: 10.1016/j.mcm.2007.12.028.
  • [8] H. Dimassi and A. Looría: Adaptive unknown-input observers-based synchronization of chaotic systems for telecommunication. IEEE Transactions on Circuits and Systems I: Regular Papers, 58(4), (2010), 800-812. DOI: 10.1109/TCSI.2010.2089547.
  • [9] A. Loría, E. Panteley, and A. Zavala-Río: Adaptive observers with persistency of excitation for synchronization of chaotic systems. IEEE Transactions on Circuits and Systems 1: Regular Papers, 56(12), (2009), 2703-2716. DOI: 10.1109/TCSI.2009.2016636.
  • [10] H. Dimassi, A. Loria, and S. Belghith: A new secured transmission scheme based on chaotic synchronization via smooth adaptive unknown-input observers. Communications in Nonlinear Science and Numerical Simulation, 17(9), (2012), 3727-3739. DOI: 10.1016/j.cnsns.2012.0L024.
  • [11] M. Ekramian, F. Sheikholeslam, S. Hosseinnia, and M.J. Yazdanpanah: Adaptive state observer for Lipschitz nonlinear systems. Systems & Control Letters, 62(4), (2013), 319-323. DOI: 10.1016/j.sysconle.2013.01.002.
  • [12] M. Yang, J. Huang, L. Yang, and M. Zhang: A note on adaptive observer design method lor one-sided Lipschitz systems. Circuits, Systems, and Signal Processing, 40 (2021), 1021-1039. DOI: 10.1007/s00034-020-01505-8.
  • [13] N. Oucief, M. Tadjine, and S. Labiod: Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems. Archives of control sciences, 26(2), (2016), 245-259. DOI: 10.1515/acsc-2016-0014.
  • [14] W-D. Chang, Sh-P. Shih, and Ch-Y. Chen: Chaotic secure communication systems with an adaptive state observer. Journal of Control Science and Engineering, 2015, Art. ID 471913, (2015). DOI: 10.1155/2015/471913.
  • [15] H. Zhang, W. Zhang, Y. Zhao, M. Ji, and L. Huang: Adaptive state observers for incrementally quadratic nonlinear systems with application to chaos synchronization. Circuits, Systems, and Signal Processing, 39(3) (2020), 1290-1306. DOI: 10.1007/s00034-019-01207-w.
  • [16] C. Cong: Observer-based robust control of uncertain systems via an integral quadratic constraint approach. International Journal of Dynamics and Control, 7(3), (2019), 926-939. DOI: 10.1007/s40435-018-00507-4.
  • [17] L. Moysis, M. Kumar Gupta, V. Mishra, M. Marwan, and Ch. Volos: Observer design for rectangular descriptor systems with incremental quadratic constraints and nonlinear outputs - Application to secure communications. International Journal of Robust and Nonlinear Control, 30(18), (2020), 8139 8158. DOI: 10.1002/rnc.5233.
  • [18] M. Ayati and H. Khaloozadeh: A stable adaptive synchronization scheme for uncertain chaotic systems via observer. Chaos, Solitons & Fractals, 42(4), (2009), 2473-2483. DOI: 10.1016/j.chaos.2009.03.108.
  • [19] J-H. Perez-Cruz, J.M. Allende Peña, Ch. Nwachioma, J. de Jesus Rubio, J. Pacheco, J.A. Meda-Campaña, D. Àvila-González, O. Guevara Galindo, I.A. Romero, and S.I. Belmonte Jiménez: A Luenberger-like observer for multistable Kapitaniak chaotic system. Complexity, 2020 Art. ID 9531431, (2020). DOI: 10.1155/2020/9531431.
  • [20] W. Zhang, Y. Zhao, M. Abbaszadeh, and M. Ji: Full-order and reduced-order exponential observers for discrete-time nonlinear systems with incremental quadratic constraints. Journal of Dynamic Systems, Measurement, and Control, 141(4), (2019). DOI: 10.1115/1.4041712.
  • [21] A. Chakrabarty, S.H. Żak, and S. Sundaram: State and unknown input observers for discrete-time nonlinear systems. In 2016 IEEE 55th Conference on Decision and Control (CDC), (2016), 7111-7116.
  • [22] Y. Zhao, W. Zhang, W Guo, S. Yu and F. Song: Exponential slate observers for nonlinear systems with incremental quadratic constraints and output nonlinearities. Journal of Control, Automation and Electrical Systems, 29(2), (2018), 127-135. DOI: 10.1007/s40313-018-0369-8.
  • [23] A. Zulfiqar, M. Rehan, and M. Abid: Observer design for one-sided Lipschitz descriptor systems. Applied Mathematical Modelling, 40(3), (2016), 2301-2311. DOI: 10.1016/j.apm.2015.09.056.
  • [24] M. Kumar Gupta, N. Kumar Tomar, and M. Darouach: Unknown inputs observer design for descriptor systems with monotone nonlinearities. International Journal of Robust and Nonlinear Control, 28(17), (2018), 5481-5494. DOI: 10.1002/rnc.4331.
  • [25] X. Fan and M. Arcak: Observer design for systems with multivariable monotone nonlinearities. Systems & Control Letters, 50(4), (2003), 319-330. DOI: 10.1016/S0167-6911(03)00170-1.
  • [26] A. Chakrabarty and M. Corless: Estimating unbounded unknown inputs in nonlinear systems. Automatica, 104 (2019), 57-66. DOI: 10.1016/j.automatica.2019.02.050.
  • [27] Y. Zhao, W. Zhang, H. Su, and J. Yang: Observer-based synchronization of chaotic systems satisfying incremental quadratic constraints and its application in secure communication. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 50(12), (2018), 5221-5232. DOI: 10.1109/TSMC.2018.2868482.
  • [28] B. Açikmeşe and M. Corless: Observers for systems with nonlinearities satisfying incremental quadratic constraints. Automatica, 47(7), (2011), 1339-1348. DOI: 10.1016/j.automatica.2011.02.017.
  • [29] T-L. Liao and Sh-H. Tsai: Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, Solitons & Fractals, 11(9), (2000), 1387-1396. DOI: 10.1016/S0960-0779(99)00051-X.
  • [30] G. Grassi, A. Ouannas, and V-T Pham: A general unified approach to chaos synchronization in continuous-time systems (with or without equilibrium points) as well as in discrete-time systems. Archives of Control Sciences, 28(1), (2018), 135-154. DOI: 10.24425/119082.
  • [31] M. Kumar Gupta, N. Kumar Tomar, and Sh. Bhaumik: Observer design for descriptor systems with Lipschitz nonlinearities: An LMI approach. Nonlinear Dynamics and System Theory, 14(3), (2014), 291-301.
Uwagi
1. This research is co-financed by Greece and the European Union (European Social Fund - ESF) through the Operational Programme “Human Resources Development, Education and Lifelong Learning” in the context of the project “Reinforcement of Postdoctoral Researchers - 2nd Cycle” (MIS 5033021), implemented by the State Scholarships Foundation (IKY). The second and the third author are supported by Science and Engineering Research Board (SERB), New Delhi, under Grant no. SGR/2019/000451.
2. Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-20179110-62c1-408e-a28f-b3916232923d
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