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Neurodynamic approaches for solving absolute value equations and circuit implementation

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  • Yu, Dongmei
  • Zhang, Gehao
  • Ma, Tiange

Abstract

The neurodynamic approaches for solving absolute value equations (AVEs) are studied. By selecting proper adaptive parameters, we propose two neurodynamic approaches: the weakly predefined-time inverse-free neurodynamic approach (WPINA) and the strongly predefined-time gradient neurodynamic approach (SPGNA). Compared to existing neurodynamic approaches for solving AVEs, the upper bounds on the convergence time of WPINA and SPGNA are not only independent of the initial conditions, but also flexible due to the dependency on only one parameter. It is noteworthy that, WPINA and SPGNA have their own advantage. The upper bound on the convergence time of SPGNA is preciser. While the advantage of WPINA is that non-differentiable absolute value term does not need to be smoothed. Additionally, WPINA can degenerate to the inverse-free neurodynamic approach (IFNA) proposed in Chen et al. (2021) when the adaptive parameter is replaced by a constant. Moreover, we introduce the circuit implementation for solving AVEs by using an absolute value circuit. Numerical simulations and an application in boundary value problems demonstrate the effectiveness of the proposed neurodynamic approaches with predefined-time convergence.

Suggested Citation

  • Yu, Dongmei & Zhang, Gehao & Ma, Tiange, 2025. "Neurodynamic approaches for solving absolute value equations and circuit implementation," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    • Handle: RePEc:eee:chsofr:v:190:y:2025:i:c:s0960077924012669
    DOI: 10.1016/j.chaos.2024.115714
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    References listed on IDEAS

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    1. Oleg Prokopyev, 2009. "On equivalent reformulations for absolute value equations," Computational Optimization and Applications, Springer, vol. 44(3), pages 363-372, December.
    2. Louis Caccetta & Biao Qu & Guanglu Zhou, 2011. "A globally and quadratically convergent method for absolute value equations," Computational Optimization and Applications, Springer, vol. 48(1), pages 45-58, January.
    3. L. Qi & D. Sun, 2002. "Smoothing Functions and Smoothing Newton Method for Complementarity and Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 121-147, April.
    4. Xiangjun Wu & Shuo Ding & Ning Xu & Ben Niu & Xudong Zhao, 2024. "Periodic event-triggered bipartite containment control for nonlinear multi-agent systems with input delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 55(10), pages 2008-2022, July.
    5. Zhao, Zhi-Ye & Jin, Xiao-Zheng & Wu, Xiao-Ming & Wang, Hai & Chi, Jing, 2022. "Neural network-based fixed-time sliding mode control for a class of nonlinear Euler-Lagrange systems," Applied Mathematics and Computation, Elsevier, vol. 415(C).
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