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Chaos Control in Delayed phase Space Constructed by the Takens' Embedding Theory

Hajiloo, Reza | 2016

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 48162 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Salarieh, Hassan; Alasty, Aria
  7. Abstract:
  8. One of the most surprising lessons of dynamical systems theory is that the phase spaces of simple nonlinear systems may contain strange attractors. For certain simple systems, such as pendulum, direct observations of the phase space and finding strange attractors are possible. But physical systems in which all the relevant dynamical variables can be simultaneously monitored are relatively scarce. Takens’ theory shows how a time-series of measurements of a single observable state can be often used to reconstruct qualitative features of the phase space of the system. In this research, using the time-series of one measurable state, an algorithm is proposed to control chaos. The approach consists of three steps: first, using the concept of Takens’ embedding theory, time-series of one measurable state is employed to reconstruct a delayed phase space preserving the topological characteristics of the unknown system. Second, a dynamic model is identified by recursive least square method to estimate the available time-series data in the delayed phase space. Finally, based on the reconstructed model, an appropriate delayed feedback controller is obtained for stabilizing unstable fixed points of the system. By taking linear Pyragas controller as a delayed feedback, the proper gains of the Pyragas controller are computed using a systematic approach. The effectiveness of the proposed algorithm is examined by applying it to some systems
  9. Keywords:
  10. Dynamics Models ; Time Series ; Chaos Control ; Delayed Feedback Control ; Delayed Phase Space

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