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Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems pp 163–174Cite as

Unknown Input Proportional Integral Observer Design for Chaotic TS Fuzzy Models

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 210))

Abstract

In this paper, the chaos synchronization problem is treated by an unknown input proportional integral observer (PIO) for a Takagi-Sugeno (TS) fuzzy chaotic model subject to unknown input and unmeasurable decision variables. This unknown input is considered like a message to encode by a chaotic system then to decode or to reconstruct by the PIO after to be transmitted by a public transmission canal in order to a secure communication system. In our case, the unknown input affects both state and output of the chaotic system. The synthesis conditions of this PIO are based on the hypothesis that the unknown input is under polynomial form with its kth derivative zero. At the end the measurable decision variables are also considered in this work like a particular case. The Lyapunov theory is used to develop the stability conditions of the unknown input PIO in LMIs formulation. A simulation example is proposed through a TS fuzzy chaotic model to validate the proposed design.

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References

  1. Jiang, G.P., Chen, G., Tang, W.K.S.: Stabilizing unstable equilibria of chaotic systems from a state observer approach. IEEE Trans. Circ. Syst. 51(6), 281–288 (2004)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Carroll, T.L., Pecora, L.M.: Synchronizing chaotic circuits. IEEE Trans. Circ. Syst. 38, 453–456 (1991)

    Article  Google Scholar 

  4. Lorenz, E.N.: Deterministic Nonperiodic Flow. J. Atmosp. Sci. 20(2), 130–141 (1963)

    Article  MathSciNet  Google Scholar 

  5. Yang, J.Z., Hu, G., Xiao, J.H.: Chaos synchronization in coupled chaotic oscillators with multiple positive Lyapunov exponents. Physical Review Letters 80(3), 496–499 (1998)

    Article  Google Scholar 

  6. Boccaletti, S., Grebogi, C., Lai, Y.C., Mancini, H., Maza, D.: The control of chos: theory and applications. Phys. Rep. 329, 103–197 (2000)

    Article  MathSciNet  Google Scholar 

  7. Boccaletti, S., Kurths, J., Osipov, G., Valladares, D.L., Zhou, C.S.: The synchronization of chaotic systems. Phys. Rep. 366, 1–101 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Shahverdiev, E.M.: Synchronization in systems with multiple time delays. Physical Review E 70(6), 67202 (2004)

    Article  Google Scholar 

  9. Xu, J.F., Min, L.Q., Chen, G.R.: A chaotic communication scheme based on generalized synchronization and hash functions. Chinese Physics Letters 21, 1445–1448 (2004)

    Article  Google Scholar 

  10. Haefner, J.W.: Modeling Biological Systems, Principles and Applications. Springer (2005)

    Google Scholar 

  11. Tao, C.H., Yang, C.D., Luo, Y., Xiong, H.X., Hu, F.: Speed feedback control of chaotic system. Chaos SolitonFract 23(1), 259–263 (2005)

    Article  MATH  Google Scholar 

  12. Yu, Y.: Adaptive synchronization of a unified chaotic system. Chaos Solitons Fractals 36(2), 329–333 (2008)

    Article  MATH  Google Scholar 

  13. Wanga, B., Wang, J., Zhong, S.M.: Impulsive Synchronization Control for Chaotic Systems. Procedia Engineering 15, 2721–2726 (2011)

    Article  Google Scholar 

  14. Gonzalo, J., Cicese, B.R., Chen, G., Shieh, L.S.: Fuzzy chaos synchronization via sampled driving signals. Int. J. Bifurcat Chaos 14, 2721–2733 (2004)

    Article  MATH  Google Scholar 

  15. Li, C., Liao, X., Wong, K.-W.: Lag synchronization of hyperchaos with application to secure communications. Chaos, Solitons and Fractals 23, 183–193 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  16. Tavazoei, M.S., Haeri, M.: Determination of active sliding mode controller parameters in synchronizing different chaotic system. Chaos, Solitons Fractals 32, 583–591 (2007)

    Article  MathSciNet  Google Scholar 

  17. Liao, T.-L., Tsai, S.-H.: Adaptive synchronization of chaotic systems and its application to secure communications. Chaos, Solitons and Fractals 11(9), 1387–1396 (2000)

    Article  MATH  Google Scholar 

  18. Cheng, C.-J.: Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication. Applied Mathematics and Computation 219, 2698–2712 (2012)

    Article  MathSciNet  Google Scholar 

  19. Cuomo, K.M., Oppenheim, A.V., Strogatz, S.H.: Synchronization of Lorenzed-based chao-tic circuits with applications to communications. IEEE Trans. Circ. Syst. II 40(10), 626–633 (1993)

    Article  Google Scholar 

  20. Dedieu, H., Kennedy, M.P., Hasler, M.: Chaos shift keying: modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuits. IEEE Trans. Circ. Syst. II 40, 634–642 (1993)

    Article  Google Scholar 

  21. Yang, T., Chua, L.O.: Secure communication via chaotic parameter modulation. IEEE Trans. Circ. Syst.I 43(9), 817–819 (1996)

    Article  Google Scholar 

  22. Takagi, T., Sugeno, M.: Fuzzy identification of systems and its application to modeling and control. IEEE Trans. Syst., Man Cybern. SCM–15(1), 116–132 (1985)

    Article  Google Scholar 

  23. Lian, K.Y., Chiu, C.S., Chiang, T.S., Liu, P.: Synthesis of fuzzy model-based design to synchronization and secure communication for chaotic systems. IEEE Trans. Syst. Man Cybern. Part B 31, 66–83 (2001)

    Article  Google Scholar 

  24. Kim, J.H., Park, C.W., Kim, E., Park, M.: Adaptive synchronization of T-S fuzzy chaotic systems with unknown parameters. Chaos, Solitons Fractals 24, 1353–1361 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Hyun, C.-H., Park, C.-W., Kim, J.-H.: Mignon Park Synchronization and secure communication of chaotic systems via robust adaptive high-gain fuzzy observer. Chaos, Solitons and Fractals 40, 2200–2209 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  27. Chen, M., Min, W.: Unknown input observer based chaotic secure communication. Physics Letters A 372, 1595–1600 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  28. Hyun, C.-H., Park, C.-W., Kim, J.-H.: Mignon Park Synchronization and secure communication of chaotic systems via robust adaptive high-gain fuzzy observer. Chaos, Solitons and Fractals 40, 2200–2209 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. Chadli, M.: Unknown input observer design for fuzzy systems with application to chaotic system reconstruction. Computers and Mathematics with Applications, 1–9 (2013)

    Google Scholar 

  30. Chadli, M., Gahinet, P.: H design with pole placement constraints: an LMI approach. IEEE Transactions on Automatic Control 41(3), 358–367 (1996)

    Article  Google Scholar 

  31. Meng, X., Yu, Y., Wen, G., Chen, R.: Chaos Synchronization of Unified Chaotic System Using Fuzzy Logic Control. In: IEEE International Conference on Fuzzy Systems, FUZZ 2008, pp. 544–547 (2008)

    Google Scholar 

  32. Tanaka, K., Ikeda, T., Wang, H.O.: A Unified Approach to Controlling Chaos viaan LMI-Based Fuzzy Control System Design. IEEE Transactions on Circuits and Systems – I: Fundamental Theory and Applications 45(10), 1021–1040 (1998)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. The Laboratory of Modeling, Information & Systems (MIS), University of Picardie Jules Verne (UPJV), 33 rue Saint-Leu, 80039, Amiens Cedex 1, France

    Mohammed Chadli

  2. The Laboratory of Automatic Applied (LAA), M’hamed Bougara University of Boumerdés (UMBB), Boumerdes, Algeria

    T. Youssef & M. Zelmat

  3. Department of Computer Science, Faculty of Electrical Engineering and Computer Science, VSB-TUO, Ostrava-Poruba, Czech Republic

    Ivan Zelinka

Authors
  1. T. Youssef
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  2. Mohammed Chadli
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  3. Ivan Zelinka
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  4. M. Zelmat
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Editor information

Editors and Affiliations

  1. Faculty of Electrical Eng. & Comp. Sci, Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Ivan Zelinka

  2. , Department of Electronic Engineering, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, China, People's Republic

    Guanrong Chen

  3. , Institute of Physical, University of Tuebingen, Auf der Morgenstelle 8, Tuebingen, 72076, Germany

    Otto E. Rössler

  4. Faculty of Electrical Eng. & Comp. Sci., Department of Computer Science, VŠB-TUO, 17. listopadu 15, Ostrava-Poruba, 708 33, Czech Republic

    Vaclav Snasel

  5. (MIR Labs), Scientific Network for Innovation, Machine Intelligence Research Labs, Auburn, 98071, Washington, USA

    Ajith Abraham

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© 2013 Springer International Publishing Switzerland

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Youssef, T., Chadli, M., Zelinka, I., Zelmat, M. (2013). Unknown Input Proportional Integral Observer Design for Chaotic TS Fuzzy Models. In: Zelinka, I., Chen, G., Rössler, O., Snasel, V., Abraham, A. (eds) Nostradamus 2013: Prediction, Modeling and Analysis of Complex Systems. Advances in Intelligent Systems and Computing, vol 210. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00542-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-00542-3_17

  • Publisher Name: Springer, Heidelberg

  • Print ISBN: 978-3-319-00541-6

  • Online ISBN: 978-3-319-00542-3

  • eBook Packages: EngineeringEngineering (R0)

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