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On the fuzzy minimum entropy control to stabilize the unstable fixed points of chaotic maps

Sadeghian, H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.apm.2010.07.036
  3. Abstract:
  4. This paper presents a fuzzy algorithm for controlling chaos in nonlinear systems via minimum entropy approach. The proposed fuzzy logic algorithm is used to minimize the Shannon entropy of a chaotic dynamics. The fuzzy laws are determined in such a way that the entropy function descends until the chaotic trajectory of the system is replaced by a regular one. The Logistic and the Henon maps as two discrete chaotic systems, and the Duffing equation as a continuous one are used to validate the proposed scheme and show the effectiveness of the control method in chaotic dynamical systems
  5. Keywords:
  6. Chaos control ; Entropy minimization ; Fuzzy system ; Chaotic dynamical systems ; Chaotic dynamics ; Chaotic map ; Chaotic trajectory ; Control methods ; Controlling chaos ; Discrete chaotic systems ; Duffing equations ; Entropy function ; Fuzzy algorithms ; Fuzzy logic algorithms ; Henon map ; Minimum entropy ; Minimum entropy control ; Shannon entropy ; Unstable fixed point ; Entropy ; Fuzzy logic ; Fuzzy sets ; Optimization ; Chaotic systems
  7. Source: Applied Mathematical Modelling ; Vol. 35, issue. 3 , 2011 , pp. 1016-1023 ; ISSN: 0307904X
  8. URL: http://www.sciencedirect.com/science/article/pii/S0307904X10002854