Reachable set bounding for delayed memristive neural networks via adaptive control

Jiemei Zhao; Ning Wu; Xiaowu Zhou; Jiemei Zhao; Ning Wu; Xiaowu Zhou

doi:10.3934/nhm.2026009

Networks and Heterogeneous Media

2026, Volume 21, Issue 1: 198-212. doi: 10.3934/nhm.2026009

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Research article

Reachable set bounding for delayed memristive neural networks via adaptive control

School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China

Received: 20 December 2025 Revised: 20 January 2026 Accepted: 27 January 2026 Published: 03 February 2026

This article is concerned with the reachable set estimation (RSE) for delayed memristive neural networks (MNNs). By exploiting the differential inclusion theory and inequality techniques, the RSE problem of MNNs was investigated. A memoryless adaptive controller was designed to realize that states of MNNs converge to a bounded region. Based on this result, an updated memoryless adaptive controller was designed, which further removed the restriction that the delay derivative must be less than 1, leading to a more general result. The new results were presented in the form of algebraic criteria, which were straightforward to verify. Ultimately, the effectiveness of the proposed criteria was demonstrated through two numerical simulations.
- memristive neural networks,
- reachable set,
- adaptive control,
- time delay,
- Filippov solution
Citation: Jiemei Zhao, Ning Wu, Xiaowu Zhou. Reachable set bounding for delayed memristive neural networks via adaptive control[J]. Networks and Heterogeneous Media, 2026, 21(1): 198-212. doi: 10.3934/nhm.2026009

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Abstract

This article is concerned with the reachable set estimation (RSE) for delayed memristive neural networks (MNNs). By exploiting the differential inclusion theory and inequality techniques, the RSE problem of MNNs was investigated. A memoryless adaptive controller was designed to realize that states of MNNs converge to a bounded region. Based on this result, an updated memoryless adaptive controller was designed, which further removed the restriction that the delay derivative must be less than 1, leading to a more general result. The new results were presented in the form of algebraic criteria, which were straightforward to verify. Ultimately, the effectiveness of the proposed criteria was demonstrated through two numerical simulations.

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