Control of Chaotic Systems with Uncertainties by Orthogonal Function Neural Network

  • Hongwei Wang
  • Shuanghe Yu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4113)


The adaptive control method based on orthogonal function neural network is proposed for a class of chaotic nonlinear systems. The adaptive controller is constructed by using a single hidden layer Chebyshev orthogonal function neural network which has advantages such as simple calculation and fast convergence. The adaptive learning law of orthogonal neural network is derived to guarantee that the adaptive weight errors and the tracking error are bounded from Lyapunov stability theory. The uncertain nonlinear system with the external disturbances can track the desired reference trajectory with bounded errors by means of the adaptive feedback controller. Based on the orthogonal function neural network, the control of chaotic systems with uncertainties is studied. The results show that the approach proposed in this paper can overcome effectively the external disturbances.


Chaotic System External Disturbance Wavelet Neural Network Uncertain Nonlinear System Lyapunov Stability Theory 
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  1. 1.
    Liu, F., Ren, Y., Shan, Z., Qiu, X.M., Li, Z.: A Linear Feedback Synchronization Theorem for AClass of Chaotic Systems. Chaos, Solution and Fractals 13(4), 723–730 (2002)zbMATHCrossRefGoogle Scholar
  2. 2.
    Shahverdiev, E.M., Sivaprakasam, S., Shore, K.A.: Lag Synchronization in Time-Delayed Systems. Physics Letter A 292(6), 320–324 (2002)zbMATHCrossRefGoogle Scholar
  3. 3.
    Li, Z., Han, C.S.: Adaptive Control for A Class of Chaotic Systems with Uncertain Parameters. Chinese Physics Transaction 5(3), 847–850 (2002)Google Scholar
  4. 4.
    Sarasola, C., Torrealdea, F.J.: Cost of Synchronizing Different Chaos Systems. Mathematics and Computers in Simulation 58(4), 309–327 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Jiang, G.P., Zheng, W.X.: An LMI Criterion for Chaos Synchronization via the Linear-State-Feedback Approach. In: IEEE International Symposium Computer Aided Control System Design, Taipei, Taiwan, pp. 368–371 (2004)Google Scholar
  6. 6.
    Grassi, G., Masolo, S.: Nonlinear Observer Design to Synchronize Hyperchaotic Systems via a Scalar Signal. IEEE Transaction of Circuits Systems 44(3), 1011–1014 (1997)CrossRefGoogle Scholar
  7. 7.
    Xie, K.M., Chen, Z.H., Xie, G.: Fuzzy Modeling Based on Rough Sets and Fuzzy Sets. In: The international Symposium on Test and Measurement, Shenzhen, pp. 977–980 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Hongwei Wang
    • 1
  • Shuanghe Yu
    • 2
  1. 1.Department of AutomationDalian University of TechnologyDalianChina
  2. 2.Automation Research CenterDalian Maritime UniversityDalianChina

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