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Attractivity of unstable equilibria for a controlled Chen system via small output feedback

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  • González, Graciela Adriana
  • Nielsen, Christopher
  • Bortoff, Zachary

Abstract

We present an output feedback controller for a single-input single-output variant of the Chen dynamical system that renders an unstable equilibrium point of the unforced system attractive using small control signals. The controller first exploits ergodicity of the unforced dynamics to asymptotically estimate the system’s state vector. Then, based on the proximity of the estimate to the desired equilibrium and a computable minimum wait time, a second stage begins applying static output error feedback. Attractivity is proven using interconnected system theory and Lyapunov analysis.

Suggested Citation

  • González, Graciela Adriana & Nielsen, Christopher & Bortoff, Zachary, 2022. "Attractivity of unstable equilibria for a controlled Chen system via small output feedback," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008219
    DOI: 10.1016/j.chaos.2022.112642
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    References listed on IDEAS

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    1. Shen, Zhiping & Li, Juntao, 2017. "Chaos control for a unified chaotic system using output feedback controllers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 208-219.
    2. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
    3. Ho, Ming-Chung & Hung, Yao-Chen & Jiang, I-Min, 2007. "On the synchronization of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 540-546.
    4. Behzad, Mehdi & Salarieh, Hassan & Alasty, Aria, 2008. "Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1295-1304.
    5. Liu, Zengrong & Li, Ying & Chen, Guanrong, 2007. "The basin of attraction of the Chen attractor," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1696-1703.
    6. Chang, Kuo-Ming, 2008. "Adaptive control for a class of chaotic systems with nonlinear inputs and disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 460-468.
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    Cited by:

    1. Remus-Daniel Ene & Nicolina Pop, 2023. "Optimal Homotopy Asymptotic Method for an Anharmonic Oscillator: Application to the Chen System," Mathematics, MDPI, vol. 11(5), pages 1-14, February.

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