Fuzzy control of dithered chaotic systems via neural-network-based approach

Feng Hsiag Hsiao*

*Corresponding author for this work

Research output: Contribution to journalJournal Article peer-review

14 Scopus citations


This paper presents an effective approach for controlling chaos. First, a neural-network (NN) model is employed to approximate the chaotic system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of an NN model. Based on the LDI state-space representation, a fuzzy controller is proposed to tame the chaotic system. If the designed fuzzy controller cannot suppress the chaos, a high frequency signal, commonly called dithers, is simultaneously injected into the chaotic system. According to the relaxed method, an appropriate dither is introduced to steer the chaotic motion into a periodic orbit or a steady state. If the frequency of dither is high enough, the trajectory described by the dithered chaotic system and that of its corresponding mathematical modelthe relaxed system can be made as close as desired. This phenomenon enables us to get a rigorous prediction of the dithered chaotic system's behavior by obtaining the behavior of the relaxed system. Finally, a numerical example with simulations is given to illustrate the concepts discussed throughout this paper.

Original languageEnglish
Pages (from-to)1114-1136
Number of pages23
JournalJournal of the Franklin Institute
Issue number7
StatePublished - 09 2010
Externally publishedYes


  • Chaos
  • Dither
  • Modeling error
  • Neural network


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