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Stabilization of multi-rotation unstable periodic orbits through dynamic extended delayed feedback control

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  • Zheng, Y.G.
  • Yu, J.L.

Abstract

The dynamic extended delayed feedback control (DEDFC) is developed to stabilize multi-rotation unstable periodic orbits (UPOs). The multi-rotation UPO here refers to the UPO that rotates more than once in a period. The DEDFC is derived by applying a dynamic control technique on the standard extended delayed feedback control (EDFC), to improve its control performance. The DEDFC is designed to meet two objectives, including enlarging the stability region of the controlled UPOs and minimizing the magnitude of the greatest Floquet multiplier. Then, a multi-objective optimization problem (MOP) is formulated for the control design and is solved with the genetic algorithm and cell mapping hybrid method. Case studies indicate that the control effect of DEDFC significantly outperforms that of standard EDFC when the control parameters are appropriately designed. The DEDFC can stabilize some multi-rotation UPOs in a large stability region. However, the standard EDFC can keep those multi-rotation UPOs stable only in a small stability region or cannot stabilize them at all.

Suggested Citation

  • Zheng, Y.G. & Yu, J.L., 2022. "Stabilization of multi-rotation unstable periodic orbits through dynamic extended delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    • Handle: RePEc:eee:chsofr:v:161:y:2022:i:c:s0960077922005720
    DOI: 10.1016/j.chaos.2022.112362
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    References listed on IDEAS

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    1. Chagas, T.P. & Toledo, B.A. & Rempel, E.L. & Chian, A.C.-L. & Valdivia, J.A., 2012. "Optimal feedback control of the forced van der Pol system," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1147-1156.
    2. de Paula, Aline Souza & Savi, Marcelo Amorim, 2009. "Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2981-2988.
    3. Pei, Lijun & Wu, Fanxin, 2021. "Periodic solutions, chaos and bi-stability in the state-dependent delayed homogeneous Additive Increase and Multiplicative Decrease/Random Early Detection congestion control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 871-887.
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