Control of continuous time chaotic systems with unknown dynamics and limitation on state measurement

[+] Author and Article Information
Hojjat Kaveh

Department of Mechanical Engineering. Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iran

Hassan Salarieh

Department of Mechanical Engineering. Sharif University of Technology, P.O. Box 11155-9567, Tehran, Iran

1Corresponding author.

ASME doi:10.1115/1.4041968 History: Received March 29, 2018; Revised November 02, 2018


This paper 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.

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