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The adaptive control of unknown chaotic systems with external disturbance via a single input

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Abstract

This paper investigates the control of chaotic systems in the presence of unknown system parameters and external disturbance. We first investigate the control of a class of special chaotic systems and then discuss the control of general chaotic systems. Some robust criteria are proposed based on adaptive control scheme. By introducing proper auxiliary variables, the stability of the closed-loop system is proved using Lyapunov stability theory. As an example to illustrate the application of the proposed method, the control of the R\(\ddot{o}\)ssler chaotic system is also investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach.

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Acknowledgments

This work was jointly supported by the National Natural Science Foundation of China under Grant Nos. 11361043 and 61304161; the Natural Science Foundation of Jiangxi Province under Grant No. 20122BAB201005 and the Scientific and Technological Project Foundation of Jiangxi Province Education Office under Grant No. GJJ14156.

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Authors and Affiliations

  1. Department of Mathematics, Nanchang University, Nanchang, 330031, People’s Republic of China

    Runzi Luo & Yanhui Zeng

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  1. Runzi Luo
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  2. Yanhui Zeng
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Correspondence to Runzi Luo.

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Luo, R., Zeng, Y. The adaptive control of unknown chaotic systems with external disturbance via a single input. Nonlinear Dyn 80, 989–998 (2015). https://doi.org/10.1007/s11071-015-1923-6

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  • DOI: https://doi.org/10.1007/s11071-015-1923-6

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