The objective of this article is to examine the complex issues associated with predefined-time synchronization (PTS) in fractional-order multimodal neural network (FOMM-NN) subject to time-varying delays. The preliminary proposition is a novel proposition regarding a PTS theorem. Subsequently, the PTS problem of FOMM-NN is analysed using the newly available judgement theorem. Based on the Lyapunov approach and on some novel analysis techniques of the fractional computation, controllers are designed in the paper in order to guarantee the synchronisation at a predefined time. Moreover, the predefined-time is established as an a freely-selected positive parameter in relevant controllers, rendering it inconsequential with respect to the initial values. It can be demonstrated that the FOMM-NN, when operated by the controllers, is capable of achieving synchronization within the predefined-time, regardless of the initial values. In the end, to validate the accuracy and effectiveness of our outcomes, we present numerical simulations that illustrate the robustness and applicability of our proposed methodology.

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The Predefined Time Stability Analysis and Synchronization Control of Fractional Order Multimodal Neural Network

  • Mengwei Niu,
  • Hui Zhao,
  • Qingjie Wang,
  • Aidi Liu,
  • Mingwen Zheng,
  • Xin Li

摘要

The objective of this article is to examine the complex issues associated with predefined-time synchronization (PTS) in fractional-order multimodal neural network (FOMM-NN) subject to time-varying delays. The preliminary proposition is a novel proposition regarding a PTS theorem. Subsequently, the PTS problem of FOMM-NN is analysed using the newly available judgement theorem. Based on the Lyapunov approach and on some novel analysis techniques of the fractional computation, controllers are designed in the paper in order to guarantee the synchronisation at a predefined time. Moreover, the predefined-time is established as an a freely-selected positive parameter in relevant controllers, rendering it inconsequential with respect to the initial values. It can be demonstrated that the FOMM-NN, when operated by the controllers, is capable of achieving synchronization within the predefined-time, regardless of the initial values. In the end, to validate the accuracy and effectiveness of our outcomes, we present numerical simulations that illustrate the robustness and applicability of our proposed methodology.