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A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Fixed-/preassigned-time synchronization for delayed complex-valued neural networks with discontinuous activations.

Leping Hu1, Lian Duan1

  • 1School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, 232001 Anhui People's Republic of China.

Cognitive Neurodynamics
|November 18, 2024
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Summary

This study achieves fixed-/preassigned-time synchronization for complex-valued neural networks with delays and discontinuous activations, independent of initial states. Novel controllers ensure faster, reliable synchronization in nonlinear systems.

Keywords:
Complex-valued neural networkDiscontinuous activationFixed-time synchronizationPreassigned-time synchronization

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Area of Science:

  • Complex Systems Dynamics
  • Nonlinear Control Theory
  • Computational Neuroscience

Background:

  • Finite-time synchronization in nonlinear systems often depends on initial states, limiting practical applications.
  • Complex-valued neural networks (CVNNs) with time delays are crucial for modeling advanced computational systems.
  • Discontinuous activation functions in CVNNs present significant challenges for synchronization analysis.

Purpose of the Study:

  • To develop novel control strategies for achieving fixed-time or preassigned-time synchronization in delayed CVNNs.
  • To eliminate the dependence of synchronization settling time on the initial states of the networks.
  • To extend existing synchronization results to CVNNs with discontinuous activation functions.

Main Methods:

  • Design of novel state feedback controllers tailored for discontinuous systems.
  • Application of Filippov regularization techniques to handle non-smooth dynamics.
  • Utilization of advanced inequality techniques for stability and synchronization analysis.
  • Explicit estimation of the upper bound for the settling time.

Main Results:

  • New criteria for achieving fixed-/preassigned-time synchronization in delayed CVNNs with discontinuous activations are established.
  • The developed methods overcome the dependency on initial states, offering practical advantages.
  • Theoretical results are shown to encompass and enhance existing findings for CVNNs with continuous activations.
  • The upper-bound of the synchronization settling time is explicitly determined.

Conclusions:

  • The proposed control approach effectively guarantees fixed-/preassigned-time synchronization for delayed CVNNs with discontinuous activations.
  • The findings provide a more robust and practical framework for synchronization in complex nonlinear systems.
  • Numerical simulations validate the theoretical results and demonstrate the efficacy of the proposed methods.