Synchronization of Neural Networks With Unbounded and Non-Differentiable Delays via Decentralized Adaptive Control

Abstract

Synchronization of delayed neural networks has been investigated in recent years via decentralized adaptive control methods. However, the effectiveness of the reported results heavily depends on the assumptions that network delays are bounded or differentiable. For more general cases involving unbounded and non-differentiable delays, it remains unclear whether the existing analytical methods and controller designs are still effective. To this end, in this article, a novel method is established to analyze the asymptotical convergence of the controlled error system with adaptive parameters by employing the differential inequality techniques for unbounded delay and Barbalat's lemma, which can effectively overcome the limitations of traditional methods in handling general delay scenarios. The theoretical results demonstrate that traditional decentralized adaptive controller for network synchronization remains effective even if the boundedness and differentiability of delay are removed. A numerical simulation further validates the effectiveness of the proposed theories.