Chaos Control in Continuous Time Systems Using Delayed Phase Space Constructed by Takens’ Embedding Theory

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Kaveh, Hojjat | 2018

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 51339 (08)
University: Sharif University of Technology
Department: Mechanical Engineering
Advisor(s): Salarieh, Hassan
Abstract:
This research has dedicated to study the control of chaos when the system dynamics is unknown and there are some limitations on measuring states. There are many chaotic systems with these features occurring in many biological, economical and mechanical systems. The usual chaos control methods do not have the ability to present a systematic control method for these kinds of systems. To fulfill these strict conditions we have employed Takens embedding theory which guarantees the preservation of topological characteristics of the chaotic attractor under an embedding named "Takens transformation". Takens transformation just needs time series of one of the measurable states. This transformation reconstructs a new chaotic attractor which is topologically similar to the unknown original attractor. After reconstructing a new attractor its governing dynamics has been identified. The measurable state of the original system which is one of the states of the reconstructed system has been controlled by delayed feedback method. Then the controlled measurable state induced stable response to all of the states of the original system
Keywords:
Chaos Control ; Delayed Feedback Control ; Time Series ; Takens Theorem ; Discrete Time Sliding Mode Control

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