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Boundary control strategy for three kinds of fractional heat equations with control-matched disturbances

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  • Cai, Rui-Yang
  • Zhou, Hua-Cheng
  • Kou, Chun-Hai

Abstract

This work aims to design the disturbance rejection controllers for three classes of fractional heat equations. Based on Filippov’s theory, the existence conclusion for the partial differential inclusion solution (PDIS) is established for fractional heat equations with discontinuous boundary conditions. Boundary control strategies are designed directly without the use of any robust control method to respectively achieve the power-law type stabilization and the asymptotical stabilization for fractional heat equations without and with time delay, respectively. A numerical example is included to illustrate the obtained results.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002393
    DOI: 10.1016/j.chaos.2021.110886
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    References listed on IDEAS

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    1. Atangana, Abdon, 2016. "On the new fractional derivative and application to nonlinear Fisher’s reaction–diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 948-956.
    2. Shukla, Manoj Kumar & Sharma, B.B., 2017. "Backstepping based stabilization and synchronization of a class of fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 274-284.
    3. Alkahtani, B.S.T. & Atangana, A., 2016. "Controlling the wave movement on the surface of shallow water with the Caputo–Fabrizio derivative with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 539-546.
    4. Shukla, Manoj Kumar & Sharma, B.B., 2017. "Stabilization of a class of fractional order chaotic systems via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 56-62.
    5. 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.
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    Cited by:

    1. Chen, Juan & Zhou, Hua-Cheng & Zhuang, Bo & Xu, Ming-Hua, 2023. "Active disturbance rejection control to stabilization of coupled delayed time fractional-order reaction–advection–diffusion systems with boundary disturbances and spatially varying coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    2. Cai, Rui-Yang & Zhou, Hua-Cheng & Kou, Chun-Hai, 2021. "Mittag-Leffler stabilization of fractional infinite dimensional systems with finite dimensional boundary controller," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 1176-1185.

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