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The Application of Accurate Exponential Solution of a Differential Equation in Optimizing Stability Control of One Class of Chaotic System

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  • Hao Jia

    (College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China
    School of Electrical Engineering, Dalian Institute of Science and Technology, Dalian 116052, China)

  • Chen Guo

    (College of Marine Electrical Engineering, Dalian Maritime University, Dalian 116026, China)

Abstract

For many nonlinear systems in our life, the chaos phenomenon generated under certain conditions in special cases will split the system and result in a crash-down of the system. This paper discusses the stable control of one class of chaotic systems and a control method based on the accurate exponential solution of a differential equation is used. Compared with other methods, the advantages are: this method determines that the system can exponentially converge at the origin and the convergence rate can be easily regulated. The chaotic system with unknown parameters is also deduced and validated by using this method. In practical application, it is found that the ship’s electric system also has the same model, so it has certain practical significance.

Suggested Citation

  • Hao Jia & Chen Guo, 2020. "The Application of Accurate Exponential Solution of a Differential Equation in Optimizing Stability Control of One Class of Chaotic System," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1740-:d:425983
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    References listed on IDEAS

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    1. Jiangbin Wang & Ling Liu & Chongxin Liu & Xiaoteng Li, 2020. "Adaptive Sliding Mode Control Based on Equivalence Principle and Its Application to Chaos Control in a Seven-Dimensional Power System," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-13, February.
    2. El-Gohary, Awad, 2006. "Optimal synchronization of Rössler system with complete uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 345-355.
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    Cited by:

    1. Francisco Ureña & Ángel García & Antonio M. Vargas, 2022. "Preface to “Applications of Partial Differential Equations in Engineering”," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

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