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PreprintCC BY 4.0arXiv

A Time-Varying Coefficient-Based Fixed-Time Neurodynamic Approach for Generalized Monotone Inclusion Problems and Its Applications

  • Vajahat Karim Khan
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Abstract

This manuscript develops time-varying coefficients neurodynamic models (TVCNDMs) to solve the inclusion problem (IPs) 0 ∈ 𝒫(w) + 𝒬(w), where 𝒫 is a maximal set-valued and 𝒬 is a single-valued operator. The underlying operators are assumed to fulfill a generalized monotonicity condition that is less restrictive than the classical monotonicity assumption. Within this framework, existence and uniqueness of the model trajectories are established, and fixed-time (FxT) convergence of the proposed TVCNDM to the solution of the IPs, along with explicit estimates of the settling time. Furthermore, the robustness of the proposed TVCNDM is investigated in the presence of bounded external disturbances, demonstrating that the FxT convergence. Numerical simulations support the theoretical results, illustrating rapid error decay and improved transient behavior achieved through the time-varying design.

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Cite

BibTeXRIS
BibTeX
@misc{khan2026timevarying,
  title = {{A Time-Varying Coefficient-Based Fixed-Time Neurodynamic Approach for Generalized Monotone Inclusion Problems and Its Applications}},
  author = {Vajahat Karim Khan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05142},
  eprint = {2610.05142},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05142},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A Time-Varying Coefficient-Based Fixed-Time Neurodynamic Approach for Generalized Monotone Inclusion Problems and Its Applications
AU  - Vajahat Karim Khan
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05142
UR  - https://arxiv.org/abs/2610.05142
AB  - This manuscript develops time-varying coefficients neurodynamic models (TVCNDMs) to solve the inclusion problem (IPs) 0 ∈ 𝒫(w) + 𝒬(w), where 𝒫 is a maximal set-valued and 𝒬 is a single-valued operator. The underlying operators are assumed to fulfill a generalized monotonicity condition that is less restrictive than the classical monotonicity assumption. Within this framework, existence and uniqueness of the model trajectories are established, and fixed-time (FxT) convergence of the proposed TVCNDM to the solution of the IPs, along with explicit estimates of the settling time. Furthermore, the robustness of the proposed TVCNDM is investigated in the presence of bounded external disturbances, demonstrating that the FxT convergence. Numerical simulations support the theoretical results, illustrating rapid error decay and improved transient behavior achieved through the time-varying design.
ER  -