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The boundary control strategy for a fractional wave equation with external disturbances

Author

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  • Jiang, Jingfei
  • Guirao, Juan Luis García
  • Chen, Huatao
  • Cao, Dengqing

Abstract

This paper is concerned with the boundary control of the fractional wave equation when the boundary is subject to persistent external disturbances. By developing the sliding mode control approach to infinite-dimensional fractional order systems, the fractional order sliding mode boundary control law is designed for the infinite dimensional setting. Moreover, based on the fractional asymptotical stability theorem, the asymptotical stability for the fractional wave equation under the control strategies proposed is addressed. Finally, numerical examples are provided to illustrate the viability of the theoretical results.

Suggested Citation

  • Jiang, Jingfei & Guirao, Juan Luis García & Chen, Huatao & Cao, Dengqing, 2019. "The boundary control strategy for a fractional wave equation with external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 92-97.
    • Handle: RePEc:eee:chsofr:v:121:y:2019:i:c:p:92-97
    DOI: 10.1016/j.chaos.2019.01.031
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    References listed on IDEAS

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    1. Jingfei Jiang & Dengqing Cao & Huatao Chen & Kun Zhao, 2017. "The vibration transmissibility of a single degree of freedom oscillator with nonlinear fractional order damping," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(11), pages 2379-2393, August.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Fágner Dias Araruna & Enrique Fernández-Cara & Luciano Cipriano Silva, 2018. "Hierarchic Control for the Wave Equation," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 264-288, July.
    4. Dadras, Sara & Momeni, Hamid Reza, 2010. "Control of a fractional-order economical system via sliding mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2434-2442.
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    Cited by:

    1. Cai, Rui-Yang & Cheng, Lan & Zhou, Hua-Cheng, 2024. "Sliding mode control for the stabilization of fractional heat equations subject to boundary uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Jiaquan Xie & Yongjiang Zheng & Zhongkai Ren & Tao Wang & Guangxian Shen, 2019. "Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions," Complexity, Hindawi, vol. 2019, pages 1-10, December.
    3. Cai, Rui-Yang & Zhou, Hua-Cheng & Kou, Chun-Hai, 2021. "Boundary control strategy for three kinds of fractional heat equations with control-matched disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).

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