Lu Chengda, Zhang Xian-Ming, Wu Min, Han Qing-Long, He Yong
IEEE Trans Cybern. 2018 Jun 8. doi: 10.1109/TCYB.2018.2836977.
This paper is concerned with energy-to-peak state estimation on static neural networks (SNNs) with interval time-varying delays. The objective is to design suitable delay-dependent state estimators such that the peak value of the estimation error state can be minimized for all disturbances with bounded energy. Note that the Lyapunov-Krasovskii functional (LKF) method plus proper integral inequalities provides a powerful tool in stability analysis and state estimation of delayed NNs. The main contribution of this paper lies in three points: 1) the relationship between two integral inequalities based on orthogonal and nonorthogonal polynomial sequences is disclosed. It is proven that the second-order Bessel-Legendre inequality (BLI), which is based on an orthogonal polynomial sequence, outperforms the second-order integral inequality recently established based on a nonorthogonal polynomial sequence; 2) the LKF method together with the second-order BLI is employed to derive some novel sufficient conditions such that the resulting estimation error system is globally asymptotically stable with desirable energy-to-peak performance, in which two types of time-varying delays are considered, allowing its derivative information is partly known or totally unknown; and 3) a linear-matrix-inequality-based approach is presented to design energy-to-peak state estimators for SNNs with two types of time-varying delays, whose efficiency is demonstrated via two widely studied numerical examples.
本文关注具有区间时变延迟的静态神经网络（SNNs）的能量到峰值状态估计。目标是设计合适的依赖延迟的状态估计器，使得对于所有具有有界能量的干扰，估计误差状态的峰值能够最小化。注意，李雅普诺夫 - 克拉索夫斯基泛函（LKF）方法加上适当的积分不等式为延迟神经网络的稳定性分析和状态估计提供了一个强大的工具。本文的主要贡献在于三点：1）揭示了基于正交和非正交多项式序列的两个积分不等式之间的关系。证明了基于正交多项式序列的二阶贝塞尔 - 勒让德不等式（BLI）优于最近基于非正交多项式序列建立的二阶积分不等式；2）采用LKF方法与二阶BLI一起推导一些新颖的充分条件，使得所得的估计误差系统全局渐近稳定并具有理想的能量到峰值性能，其中考虑了两种时变延迟，允许其导数信息部分已知或完全未知；3）提出了一种基于线性矩阵不等式的方法来设计具有两种时变延迟的SNNs的能量到峰值状态估计器，通过两个广泛研究的数值例子证明了其有效性。
