A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Advanced Search
Volume 6 Issue 3
May  2019

IEEE/CAA Journal of Automatica Sinica

  • JCR Impact Factor: 15.3, Top 1 (SCI Q1)
    CiteScore: 23.5, Top 2% (Q1)
    Google Scholar h5-index: 77， TOP 5
Turn off MathJax
Article Contents
Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2019  >  6(3): 816-823
Khatir Khettab, Samir Ladaci and Yassine Bensafia, "Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 816-823, May 2019. doi: 10.1109/JAS.2016.7510169
Citation: Khatir Khettab, Samir Ladaci and Yassine Bensafia, "Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain," IEEE/CAA J. Autom. Sinica, vol. 6, no. 3, pp. 816-823, May 2019. doi: 10.1109/JAS.2016.7510169
shu

Fuzzy Adaptive Control of a Fractional Order Chaotic System With Unknown Control Gain Sign Using a Fractional Order Nussbaum Gain

doi: 10.1109/JAS.2016.7510169
  • 1.

    Electrical Engineering Department, University of Mohamed Boudiaf, M'sila 28000, Algeria

  • 2.

    Electrical Engineering Department, University of Skikda, Skikda 21000, Algeria

  • 3.

    EEA Department, National Polytechnic School of Constantine, B. P. 75 A, Ali Mendjli 25000 Constantine, Algeria

  • 4.

    SP-Lab Laboratory, Department of Electronics, Mentouri University, Route de Ain Elbey, Constantine 25000, Algeria

  • 5.

    Electrical Engineering Department, University of Bouira, 10000 Bouira, Algeria

Funds:

the Algerian Ministry of Higher Education and Scientific Research (MESRS) for CNEPRU Research Project A01L08UN210120110001

More Information
    Abstract
  • In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order (SISO) systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbaum gain. Based on Lyapunov stability theorem, stability analysis is performed for the proposed control method for an acceptable synchronization error level. In this work, the Grünwald-Letnikov method is used for numerical approximation of the fractional order systems. A simulation example is given to illustrate the effectiveness of the proposed control scheme.

     

    • FullText(HTML)
  • loading
    • References(34)
  • [1]
    I. Petráš s, "A note on the fractional-order Chua's system, " Chaos, Solitons and Fractals, vol. 38, no. 1, pp. 140-147, 2008. doi: 10.1016/j.chaos.2006.10.054
    [2]
    X. Gao and J. Yu, "Chaos in the fractional order periodically forced complex Duffing's oscillators, " Chaos, Solitons and Fractals, vol. 24, no. 4, pp. 1097-1104, 2005. doi: 10.1016/j.chaos.2004.09.090
    [3]
    K. Rabah, S. Ladaci, and M. Lashab, "Stabilization of Fractional Chen Chaotic System by Linear Feedback Control, " in Proc. 3rd Int. Conf. Control, Eng. & Information Technology, CEIT' 2015, Tlemcen, Algeria. IEEE, 25-27, May 2015.
    [4]
    W. H. Deng and C. P. Li, "Chaos synchronization of the fractional Lü system, " Physica A, vol. 353, no. 1, pp. 61-72, 2005. http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_063fd84ed5be9d309335c6de6a06404f
    [5]
    T. L. Lin and C. -H. Kuo, "$H^{infty}$ synchronization of uncertain fractional order chaotic systems: adaptive fuzzy approach, " ISA Trans., vol. 50, pp. 548-556, 2011. doi: 10.1016/j.isatra.2011.06.001
    [6]
    K. Rabah, S. Ladaci, and M. Lashab, "State feedback with fractional $PI^{lambda}D^{mu}$ control structure for Genesio-Tesi Chaos stabilization, " in Proc. 15th IEEE Int. Conf. Sciences and Techniques of Autom. Control & Computer Eng., STA'2015, Monastir, Tunisia: IEEE, 21-23 December 2015, 328-333.
    [7]
    S. Ladaci and A. Charef, "On fractional adaptive control, " Nonlinear Dynamics, vol. 43, no. 4, pp. 365-378, 2006. doi: 10.1007/s11071-006-0159-x
    [8]
    S. Ladaci, J. J. Loiseau, and A. Charef, "Adaptive internal model control with fractional order parameter, " Int. J. Adaptive Control and Signal Processing, vol. 24, no. 11, pp. 944-960, 2010. doi: 10.1002/acs.v24:11
    [9]
    S. Ladaci and K. Khettab, "Fractional order multiple model adaptive control, " Int. J. Autom. & Syst. Eng., vol. 6, no. 2, pp. 110-122, 2012. http://d.old.wanfangdata.com.cn/NSTLHY/NSTL_HYCC027636376/
    [10]
    Y. Li, Y. -Q. Chen, and Y. Cao, "Fractional order universal adaptive stabilization, " in Proc. 3rd IFAC Workshop on Fractional Differentiation and Its Applications, Ankara, Turkey, November 2008, pp. 5-7.
    [11]
    L. X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Englewood Cliffs, NJ: Prentice-Hall, 1994.
    [12]
    L. X. Wang, "Stable adaptive fuzzy control of nonlinear systems, " IEEE Trans. Fuzzy Syst., vol. 1, no. 2, pp. 146-155, 1993. doi: 10.1109/91.227383
    [13]
    K. Khettab, Y. Bensafia, and S. Ladaci, "Robust adaptive fuzzy control for a class of uncertain nonlinear fractional system, " in Proc. 2nd Int. Conf. Electrical Eng. and Control Applications, Constantine, Algeria, November 2014.
    [14]
    R. D. Nussbaum, "Some remarks on the conjecture in parameter adaptive control, " Syst. & Control Letters, vol. 3, no. 5, pp. 243-246, 1983. http://www.sciencedirect.com/science/article/pii/016769118390021X
    [15]
    X. D. Ye and J. P. Jiang, "Adaptive nonlinear design without a priori knowledge of control directions, " IEEE Trans. Autom. Control, vol. 43, no. 11, pp. 1617-1621, 1998. doi: 10.1109/9.728882
    [16]
    J. C. Willems and C. I. Byrnes, "Global adaptive stabilization in the absence of information on the sign of the high frequency gain, " Lecture Notes in Control and Information Sciences, Berlin, Springer-Verlag, vol. 62, pp. 49-57, 1984.
    [17]
    B. Martesson, "Remarks on adaptive stabilization of first order nonlinear systems, " Syst. and Control Letters, vol. 14, no. 1, pp. 1-7, 1990. doi: 10.1016/0167-6911(90)90073-4
    [18]
    Y. Zhang, C. Y. Wen, and Y. C. Soh, "Adaptive backstepping control design for systems with unknown high-frequency gain, " IEEE Trans. Autom. Control, vol. 45, no. 12, pp. 2350-2354, 2000. doi: 10.1109/9.895572
    [19]
    Y. -J. Liu and Z. -F. Wang, "Adaptive fuzzy controller design of nonlinear systems with unknown gain sign, " Nonlinear Dynamics, vol. 58, no. 4, pp. 687-695, 2009. doi: 10.1007/s11071-009-9510-3
    [20]
    A. Boulkroune and M. M'saad, "On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign, " Fuzzy Sets and Syst., vol. 201, pp. 71-85, 2012. doi: 10.1016/j.fss.2011.12.005
    [21]
    K. B. Oldham and J. Spanier, The Fractional Calculus. New York: Academic Press, 1974.
    [22]
    K. Diethelm, N. J. Ford, and A. D. Freed, "A predictor-corrector approach for the numerical solution of fractional differential equations, " Nonlinear Dynamics, vol. 29, no. 1-4, pp. 3-22, 2002. doi: 10.1023/A:1016592219341
    [23]
    Y. Bensafia, S. Ladaci, and K. Khettab, "Using a fractionalized integrator for control performance enhancement, " Int. J. Innovative Computing, Information and Control, vol. 11, no. 6, pp. 2013-2028, 2015. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=b88a1ff20752540c42eb290c6d500d6d
    [24]
    R. Caponetto, G. Dongola, L. Fortina, and I. Petráš s, "Fractional order systems: modeling and control application, " World Scientific Series on Nonlinear Science, Series A, vol. 72, pp. 62-65, 2010. http://d.old.wanfangdata.com.cn/Periodical/zdhxb201411004
    [25]
    E. Nechadi, M. N. Harmas, N. Essounbouli, and A. Hamzaoui, "Adaptive fuzzy sliding mode power system stabilizer using Nussbaum gain, " Int. J. Autom. Computing, vol. 10, no. 4, pp. 281-287, 2013. doi: 10.1007/s11633-013-0722-0
    [26]
    S. S. Ge, C. Yang, and T. H. Lee, "Adaptive robust control of a class of nonlinear strict-feedback discrete-time systems with unknown control directions, " Syst. & Control Letters, vol. 57, no. 11, pp. 888-895, 2008. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=f6035cdba163654102d1447f23a81921
    [27]
    S. S. Ge and J. Wang, "Robust adaptive tracking for time-varying uncertain nonlinear systems with unknown control coefficients, " IEEE Trans. Automatic Control, vol. 48, no. 8, pp. 1463-1469, 2003. doi: 10.1109/TAC.2003.815049
    [28]
    L. Li and Y. G. Sun, "Adaptive fuzzy control for nonlinear fractional-order uncertain systems with unknown uncertainties and external disturbance, " Entropy, vol. 17, no. 12, pp. 5580-5592, 2015. doi: 10.3390/e17085580
    [29]
    T. T. Georgiou and M. C. Smith, "Robustness analysis of nonlinear feedback systems: an input-output approach, " IEEE Trans. Automatic Control, vol. 42, no. 9, pp. 1200-1221, 1997. doi: 10.1109/9.623082
    [30]
    T. C. Lin, C. H. Wang, and H. L. Liu, "Observer-based indirect adaptive fuzzy-neural tracking control for nonlinear SISO systems using VSS and $H^{infty}$ approaches, " Fuzzy Sets and Syst., vol. 143, pp. 211-232, 2004. doi: 10.1016/S0165-0114(03)00167-2
    [31]
    N. Aguila-Camacho, M. A. Duarte-Mermoud, and J. A. Gallegos, "Lyapunov functions for fractional order systems, " Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 2951- 2957, 2014. doi: 10.1016/j.cnsns.2014.01.022
    [32]
    M. A. Duarte-Mermoud, N. Aguila-Camacho, J. A. Gallegos, and R. Castro-Linares, "Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems, " Communications in Nonlinear Science and Numerical Simulation, vol. 22, no. 1-3, pp. 650-659, 2015. doi: 10.1016/j.cnsns.2014.10.008
    [33]
    J. A. Gallegos, M. A. Duarte-Mermoud, N. Aguila-Camacho, and R. Castro-Linares, "On fractional extensions of Barbalat Lemma, " Syst. & Control Letters, vol. 84, pp. 7-12, Oct. 2015. http://www.sciencedirect.com/science/article/pii/S0167691115001413
    [34]
    C. L. Tsung and V. E. Balas, "Fractional order chaotic system tracking design based on adaptive hybrid intelligent control, " in Proc. the IEEE Int. Conf. Fuzzy Syst., Taipei, China, Jun. 2011.
    • Related Articles
    • Supplements(0)

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Figures(7)

    Get Citation
    PDF
    XML

    Article Metrics

    Article views (1459) PDF downloads(69) Cited by()

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return