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Synchronizaion of Chaotic Systems by Using Fractional Calculus

Gomroki, Mehdi | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44813 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Salarieh, Hassan
  7. Abstract:
  8. Synchronization means to control the response system to follow the drive system. It first began in 1990 in a paper by Pecora and after that it is used in many applications like secure communication. Another application for synchronization which is introduced here is identification of chaotic systems. According to the research done, this application hasn’t been in the literature as it is known to us. Synchronization papers usually devide into two parts. In one of them the parameters of the systems are unknown, so adaptive laws are used to estimate the parameters. In the other part, the parameters are taken known. It is not mentioned in the first group that the estimation would converge to the correct value of the parameters. The transient part of solution in many papers for identical and nonidentical synchronization is not proper and usually it has many fluctuations or long settling time. So the goal of this research is to fractional calculation use to improve the transient behavior of the solution like reducing settling time and fluctuations in synchronization errors and parameters estimation. Also according to complication of the stability theorems in fractional calculus, a stability analisys for the controlled systems is done.
    As it is mentioned in this research two applications for synchronization is studied. The first one is identification of the chaotic systems using fractional calculus. In this application it is necessary to prove that the parameters estimation would converge to the correct value of them. The other application is secue communication using the identification mentioned before
  9. Keywords:
  10. Adaptive Control ; Chaos Synchronization ; Chaotic System Identification ; Fractional Order Calculus Dynamic ; Secure Communication

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