This paper discusses the reachable set estimation problem of neural networks with mixed delays. Firstly, by means of the maximal Lyapunov-Krasovskii functional, we obtain a non-ellipsoid form of the reachable set. Further more, when calculating the derivative of the maximum Lyapunov functional, the lower bound lemma and reciprocally convex approach method are used to solve the reciprocally convex combination term, which reduce the related decision variables. Secondly, we extend the results to polytopic uncertainties neural networks and consider the case of uncertain differentiable parameters. Finally, two numerical examples and one application example are listed to show the validity of our methods.

中文翻译：

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具有混合延迟的神经网络的可到达集边界：双向凸方法。

本文讨论了混合时滞神经网络的可达集估计问题。首先，借助最大的Lyapunov-Krasovskii泛函，我们获得了可达集的非椭球形式。此外，在计算最大Lyapunov泛函的导数时，采用下界引理和倒凸方法来求解倒凸组合项，从而减少了相关的决策变量。其次，我们将结果扩展到多主题不确定性神经网络，并考虑不确定可微参数的情况。最后，列举了两个数值示例和一个应用示例，以证明我们方法的有效性。