Loading...

Stabilizing Periodic Orbits of Fractional Order Chaotic Systems Via Linear State Feedback Control

Rahimi, Mohammad Amin | 2010

986 Viewed
  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40973 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Salarieh, Hassan; Alasty, Aria
  7. Abstract:
  8. Stabilizing periodic orbit of fractional order chaotic system via linear state feedback is the subject of this research. Firstly, for detection of the unstable periodic orbits (UPO) in fractional order chaotic systems, the famous shooting method for integer order systems is extended to fractional order systems. After that, for stabilizing the fractional order system a hypothesis is stated and a theorem is proved in a specific condition. Besides the proven theorem, some examples are presented as evidences that verify the hypothesis. So, through the hypothesis, common methods for stabilizing integer order systems can be extended to the fractional order systems. Finally, for stabilizing the UPO’s, the linearization method on the periodic orbit is employed. The linearized system will be a fractional order linear time varying one. On the basis of the hypothesis, stability theorems of the integer order linear time varying system can be used. After all, these methods are applied to the van der Pol and Duffing fractional order chaotic systems as demonstrative examples. Furthermore, a common non-linear controller, called sliding mode is developed for stabilizing the UPO’s of fractional order systems and the results are presented for the van der Pol and Duffing systems.

  9. Keywords:
  10. Fractional Order System ; Control ; Unstable Periodic Orbit ; Chaos Theory ; Linear Stability

 Digital Object List

 Bookmark