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Adaptive fuzzy echo state network optimal synchronization control of hybrid–order chaotic systems via reinforcement learning

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  • Zhong, Mei
  • Huang, Chengdai
  • Cao, Jinde
  • Liu, Heng

Abstract

In this paper, a novel optimal synchronization control scheme for fractional–integer hybrid–order chaotic systems is formulated. To deal with the fractional–order (FO) constraint, a transformation programme is developed and then the master system considered as an FO chaotic system is transformed into an integer–order one. A fuzzy echo state network (FESN) with the advantages of both fuzzy logic system and echo state network is introduced to approximate system uncertainty. Simultaneously, to alleviate the resource pressure, an optimal synchronization control is proposed in the light of the reinforcement learning mechanism, in which critic–actor update laws are constructed through the negative gradient of a positive function with regard to Bellman residual. Compared to typical fuzzy synchronization control, the devised FESN synchronization scheme with the same computational complexity possess superior approximation ability and synchronization performance. Ultimately, three simulation cases are exhibited to check the validity of the proposed approach.

Suggested Citation

  • Zhong, Mei & Huang, Chengdai & Cao, Jinde & Liu, Heng, 2024. "Adaptive fuzzy echo state network optimal synchronization control of hybrid–order chaotic systems via reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    • Handle: RePEc:eee:chsofr:v:181:y:2024:i:c:s0960077924002170
    DOI: 10.1016/j.chaos.2024.114665
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    References listed on IDEAS

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    1. Hu, Huanling & Wang, Lin & Lv, Sheng-Xiang, 2020. "Forecasting energy consumption and wind power generation using deep echo state network," Renewable Energy, Elsevier, vol. 154(C), pages 598-613.
    2. Hallaji, Majid & Dideban, Abbas & Khanesar, Mojtaba Ahmadieh & kamyad, Ali vahidyan, 2018. "Optimal synchronization of non-smooth fractional order chaotic systems with uncertainty based on extension of a numerical approach in fractional optimal control problems," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 325-340.
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