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<p>This paper proposes a relaxed Lyapunov-based framework for fixed-time synchronization of fuzzy inertial neural networks (FINNs) with time-varying delays through the synergistic combination of adaptive and pinning control. A time-dependent control architecture is established that incorporates both adaptive parametric tuning and selective node actuation, while circumventing traditional matrix inequality constraints via algebraic synchronization criteria. The key innovation lies in the relaxation of Lyapunov derivative conditions, where non-strict negative definiteness is permitted while maintaining fixed-time attractivity, thereby significantly expanding the method’s applicability domain. Theoretical derivations demonstrate that synchronization is guaranteed within a fixed-time horizon independent of initial conditions, with the convergence upper bound explicitly quantified. Comprehensive numerical validations confirm the framework’s effectiveness in achieving accelerated synchronization. The proposed methodology bridges theoretical rigor and practical implementability for complex neurodynamic systems under fuzzy operations and spatiotemporal uncertainties.</p>

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Relaxed Lyapunov-based fixed-time synchronization of fuzzy inertial neural networks via adaptive and pinning control

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Jun Liu,
  • Kaibo Shi

摘要

This paper proposes a relaxed Lyapunov-based framework for fixed-time synchronization of fuzzy inertial neural networks (FINNs) with time-varying delays through the synergistic combination of adaptive and pinning control. A time-dependent control architecture is established that incorporates both adaptive parametric tuning and selective node actuation, while circumventing traditional matrix inequality constraints via algebraic synchronization criteria. The key innovation lies in the relaxation of Lyapunov derivative conditions, where non-strict negative definiteness is permitted while maintaining fixed-time attractivity, thereby significantly expanding the method’s applicability domain. Theoretical derivations demonstrate that synchronization is guaranteed within a fixed-time horizon independent of initial conditions, with the convergence upper bound explicitly quantified. Comprehensive numerical validations confirm the framework’s effectiveness in achieving accelerated synchronization. The proposed methodology bridges theoretical rigor and practical implementability for complex neurodynamic systems under fuzzy operations and spatiotemporal uncertainties.