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Nonlinear Dynamics

, Volume 83, Issue 3, pp 1601–1619 | Cite as

An extended Neuro-Fuzzy-based robust adaptive sliding mode controller for linearizable systems and its application on a new chaotic system

  • Baraka Olivier Mushage
  • Jean Chamberlain Chedjou
  • Kyandoghere Kyamakya
Original Paper

Abstract

In this paper, a new approach based on neuro-fuzzy systems is proposed to efficiently address some well-known and challenging problems related to the design and implementation of efficient (i.e. accurate, robust and stable) controllers for nonlinear and chaotic systems subject to external disturbances and uncertain dynamics. To tackle the uncertainty problem, a neuro-fuzzy system is used to approximate the uncertain dynamics. Considering the risk that the control gain function can be close or equal to zero, this issue is addressed in order to guaranty singularity avoidance in the control law. The proposed approach guarantees that the estimation errors and external disturbances cannot affect the stability of the control system. This approach ensures that the control action remains realistic in its characteristics such as amplitude and frequency. Another contribution of this paper is to demonstrate the application of the proposed approach to the control of a new system exhibiting a strange bifurcation scenario characterized by a transition from transient chaos to torus states. As proof of concepts in order to validate the approach, a benchmarking is performed, leading to a comparison of the proposed approach with two neural networks-based controllers recently presented in the literature. Specifically, all the three aforementioned controllers are applied to a nonlinear system used in the literature and it is clearly demonstrated how the proposed controller outperforms its counterparts. The performance criteria (of controllers) are expressed in terms of metrics like the control signal, and the controllers’ performances in both transient and steady states.

Keywords

Neuro-fuzzy system Adaptive SMC Robust control Linearizable system Chaotic system  

References

  1. 1.
    Ruihong, L., Shuang, L.: Chaos control and synchronization of the \(\varPhi ^6\)- Van der Pol system driven by external and parametric excitations. Nonlinear Dyn. 53, 261–271 (2008)CrossRefMATHGoogle Scholar
  2. 2.
    Xiang-Jun, W., Jing-Sen, L., Guan-Rong, C.: Chaos synchronization of Rikitake chaotic attractor using the passive control technique. Nonlinear Dyn. 53, 45–53 (2008)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Wang, H., Han, Z., Xie, Q.: Finite-time chaos control of unified chaotic systems with uncertain parameters. Nonlinear Dyn. 55, 323–328 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Shi, X., Wang, Z.: Robust chaos synchronization of four-dimensional energy resource system via adaptive feedback control. Nonlinear Dyn. 60, 631–637 (2010)CrossRefMATHGoogle Scholar
  5. 5.
    Farivar, F., Shoorehdeli, M.A., Nekoui, M.A., Teshnehlab, M.: Chaos control and modified projective synchronization of unknown heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive backstepping control. Nonlinear Dyn. 67, 1913–1941 (2012)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Kengne, J., Chedjou, J.C., Fono, V.A., Kyamakya, K.: On the analysis of bipolar transistor based chaotic circuits: case of a two-stage colpits oscillator. Nonlinear Dyn. 67, 1247–1260 (2012)CrossRefGoogle Scholar
  7. 7.
    Kengne, J., Chedjou, J.C., Kom, M., Kyamakya, K., Tamba, V.K.: Regular oscillations, chaos, and multistability in a system of two coupled van der Pol oscillators: numerical and experimental studies. Nonlinear Dyn. 76, 1119–1132 (2014)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Chedjou, J.C., Kana, L.K., Moussa, I., Kyamakya, K., Laurent, A.: Dynamics of quasiperiodically forced Rayleigh oscillator. J. Dyn. Syst. Meas. Control Trans. ASME 128, 600–607 (2006)CrossRefGoogle Scholar
  9. 9.
    Dadras, S., Momeni, H.R.: Adaptive sliding mode control of chaotic dynamical systems with application to synchronization. Math. Comput. Simul. 80, 2245–2257 (2010)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Mou, C., Chang-sheng, J., Bin, J., Qing-xian, W.: Sliding mode synchronization controller design with neural network for uncertain chaotic systems. Chaos Solitons Fractals 39, 1856–1863 (2009)CrossRefMATHGoogle Scholar
  11. 11.
    Zeng, X.-J.: A Comparison between T-S fuzzy systems and affine T-S fuzzy systems as nonlinear control system models. In: 2014 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), Beijing (2014)Google Scholar
  12. 12.
    Seng, T.L., Khalid, M., Yusof, R., Omatu, S.: Adaptive neuro-fuzzy control system by RBF and GRNN neural networks. J. Intell. Robot. Syst. 23, 267–289 (1998)CrossRefMATHGoogle Scholar
  13. 13.
    Li, I.-H., Lee, L.-W., Chiang, H.-H., Chen, P.-C.: Intelligent switching adaptive control for uncertain nonlinear dynamical systems. Appl. Soft Comput. 34, 638–654 (2015)CrossRefGoogle Scholar
  14. 14.
    Pan, Y.: Simplified adaptive neural control of strict-feedback nonlinear systems. Neurocomputing 159, 251–256 (2015)CrossRefGoogle Scholar
  15. 15.
    Cui, Y., Zhang, H., Wang, Y., Zhang, Z.: Adaptive neural dynamic surface control for a class of uncertain nonlinear systems with disturbances. Neurocomputing 165, 152–158 (2015)CrossRefGoogle Scholar
  16. 16.
    Lazzerini, B., Reyneri, L., Chiaberge, M.: A neuro-fuzzy approach to hybrid intelligent control. IEEE Trans. Ind. Appl. 35, 413–425 (1999)CrossRefGoogle Scholar
  17. 17.
    Andrievskii, B.R., Fradkov, A.L.: Control of chaos: methods and applications. Autom. Remote Control 64, 673–713 (2003)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Alvarez-Ramirez, J., Espinosa-Paredes, G., Puebla, H.: Chaos control using small-amplitude damping signals. Phys. Lett. A 316, 196–205 (2003)CrossRefMATHGoogle Scholar
  19. 19.
    Feki, M.: An adaptive feedback control of linearizable chaotic systems. Chaos Solitons Fractals 15, 883–890 (2003)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Chedjou, J.C., Fotsin, H.B., Waofo, P., Domngang, S.: Analog simulation of the dynamics of a van der pol oscillator coupled to a duffing oscillator. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 48, 748–757 (2001)CrossRefMATHGoogle Scholar
  21. 21.
    Chedjou, J.C., Kyamakya, K.: A universal concept based on cellular neural networks for ultrafast and flexible solving of differential equations. IEEE Trans. Neural Netw. Learn. Syst. 26, 749–762 (2015)CrossRefGoogle Scholar
  22. 22.
    Lu, Q., Sun, Y., Mei, S.: Nonlinear Control Systems and Power System Dynamics, vol. 371. Kluwer Academic Publisher, Massachusetts (2010)Google Scholar
  23. 23.
    Hojati, M., Gazor, S.: Hybrid adaptive fuzzy identification and control of nonlinear systems. IEEE Trans. Fuzzy Syst. 10, 198–210 (2002)CrossRefGoogle Scholar
  24. 24.
    Li, C., Lee, C.-Y.: Self-organizing neuro-fuzzy system for control of unknown plants. IEEE Trans. Fuzzy Syst. 11, 135–150 (2003)CrossRefGoogle Scholar
  25. 25.
    Kayacan, E., Erdal, K., Ramon, H., Saeys, W.: Adaptive neuro-fuzzy control of a spherical rolling robot using sliding-mode-control-theory-based online learning algorithm. IEEE Trans. Cybern. 43, 170–179 (2013)CrossRefGoogle Scholar
  26. 26.
    Nagarale, R.M., Patre, B.M.P.: Decoupled Neural fuzzy sliding mode control of nonlinear systems. In: 2013 IEEE International Conference on Fuzzy Systems (FUZZ), Hyderabad (2013)Google Scholar
  27. 27.
    Liu, J., Wang, X.: Advanced Sliding Mode Control for Mechanical Systems, vol. 362. Springer, Berlin (2012)MATHGoogle Scholar
  28. 28.
    Zhu, C., Liu, Y., Guo, Y.: Theoretic and numerical study of a new chaotic system. Intell. Inf. Manag. 2, 104–109 (2010)Google Scholar
  29. 29.
    Cherban, D.N.: Global Attractors of Non-Autonomous Dissipative Dynamical Systems. World Scientific, Singapore (2014)Google Scholar
  30. 30.
    Vaidyanathan, S., Madhavan, K.: Adaptive control of a two-scroll novel chaotic system with a quadratic nonlinearity. In: International Conference on Science, Engineering and Management Research (ICSEMR 2014), Chennai (2014)Google Scholar
  31. 31.
    Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents from a time series. Phys. D 16, 285–317 (1985)Google Scholar
  32. 32.
    Vaidyanathan, S.: Analysis of two novel chaotic systems with a hyperbolic sinusoidal nonlinearity and their adaptive chaos synchronization. In: Fourth International Conference on Computing, Communications and Networking Technologies (ICCCNT), Tiruchengode (2013)Google Scholar
  33. 33.
    Ge, S.S., Wang, C.: Direct adaptive NN control of a class of nonlinear systems. IEEE Trans. Neural Netw. 13, 214–221 (2002)CrossRefGoogle Scholar
  34. 34.
    Skogestad, S.: Simple analytic rules for model reduction and PID controller tuning. J. Process Control 13, 291–309 (2003)CrossRefGoogle Scholar
  35. 35.
    Chakravarty, A., Mahanta, C.: Actuator fault tolerant control scheme for nonlinear uncertain systems using backstepping based sliding mode. In: 2013 Annual IEEE India Conference (INDICON), (2013)Google Scholar
  36. 36.
    Nguyen, T.-B.-T., Liao, T.-L., Yan, J.-J.: Improved adaptive sliding mode control for a class of uncertain nonlinear systems subjected to input nonlinearity via fuzzy neural networks. Math. Probl. Eng. 2015, 1–13 (2015)Google Scholar
  37. 37.
    Chueshov, I.D.: Introduction to the Theory of Infinite-Dimensional Dissipative Systems. ACTA Scientific Publishing House, Kharkiv (2002)MATHGoogle Scholar
  38. 38.
    Cuesta, F., Anibal, O.: Intelligent Mobile Robot Navigation, Star springer tracts in advanced Robotics. Springer, New York. ISBN 3-540-23956-1 (2005)Google Scholar
  39. 39.
    Li, Z., Halang, W.A., Chen, G.: Integration of Fuzzy Logic and Chaos Theory, studies in Fuzziness and Soft Computing. Springer, New York. ISBN 3-540-26899-5 (2008)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Baraka Olivier Mushage
    • 1
  • Jean Chamberlain Chedjou
    • 1
  • Kyandoghere Kyamakya
    • 1
  1. 1.Institute of Smart Systems TechnologiesUniversity of KlagenfurtKlagenfurtAustria

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