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Chaotification of Dynamic Systems with Adaptive Linear Feedback of Available State Variables

Abediny NajafAbadi, Mohammad | 2009

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 40244 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Alasty, Aria; Salarieh, Hassan
  7. Abstract:
  8. In this thesis, chaotification of dynamic systems in general and chaotification via full state linear feedback are investigated particularly. Studying chaotification is a problem over investigating dynamics of chaos and controlling it, so studying this problem needs to have some general information about chaos and its dynamics. Because, this is a new case, researches in this field are not enough and actually, there is no paper on application of chaotification. Reviewing literature in this field shows that in solving problems of chaotification, there is no notice on applications and ability to apply it on physical systems. So one of the most important aims of this thesis, is to find an applicable method to chaotify dynamic systems in general form. In the research process, first by reviewing literature, a new method was introduced in chaotification with only feedback of available state variables. In this method, the controller gains are high and a type of nonlinear fold function is used to enforce system trajectories to be in a bounded space, so its experimental aspect is weak. By using systems with chaotic nature but with non-chaotic parameters like logistic map, we can reduce in controller gain, and fold function can be removed or applied only on controller. In the next, by using a feed-forward control algorithm, Lyapunov exponents of the system was controlled and placed, so placing positive numbers for Lyapunov exponents of an stable linear system leads to chaos. In the other chapter, behavior of continuous time system in presence of time-delayed feedback was studied. Using this idea, the chaotification in continuum media was introduced. By using a time-delayed feedback and a type of boundary control on systems with PDE characteristic equation, an unstable wave in continuum medium was chaotificated. The most important point in all of the introduced methods, is the ability of using these methods in engineering applications.
  9. Keywords:
  10. Dynamical Systems ; Lyapunov Exponent ; Chaotification ; Linear Feedback ; Chaos Dynamics

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