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Technical Brief

The Control and Synchronization of a Rotational Relativistic Chaotic System With Parameter Uncertainties and External Disturbance

[+] Author and Article Information
Runzi Luo, Yanhui Zeng

Department of Mathematics,
Nanchang University,
Nanchang 330031, China

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 5, 2014; final manuscript received January 25, 2015; published online June 9, 2015. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 10(6), 064503 (Nov 01, 2015) (6 pages) Paper No: CND-14-1281; doi: 10.1115/1.4029702 History: Received November 05, 2014; Revised January 25, 2015; Online June 09, 2015

This paper investigates the control and synchronization of a rotational relativistic chaotic system with parameter uncertainties and external disturbance. By using the proper coordinate transformation, some novel criteria for control or synchronization are proposed via a single input. Numerical simulations are given to show the robustness and efficiency of the proposed approach.

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Figures

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Fig. 1

The chaotic attractor of system (1). (a) Chaotic attractor in (x1; x2; x4) space and (b) chaotic attractor in (x4; x3; x2) space.

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Fig. 2

The phase diagram of system (3). (a) The phase diagram in (x1; x2; x4) space and (b) the phase diagram in (x2; x3; x4) space.

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Fig. 3

The time response of states x1, x2, x3, x4 of system (3)

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Fig. 4

The time evolution of estimated values p∧1,q∧1

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Fig. 5

The time response of controller u

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Fig. 6

The synchronization errors between systems (2) and (13)

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Fig. 7

The time evolution of estimated values p∧1,q∧1

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Fig. 8

The time evolution of estimated values p∧2,q∧2

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