IEEE Trans Neural Netw Learn Syst. 2021 Aug;32(8):3553-3565. doi: 10.1109/TNNLS.2020.3015376. Epub 2021 Aug 3.
In this article, a novel proportional-integral observer (PIO) design approach is proposed for the nonfragile H state estimation problem for a class of discrete-time recurrent neural networks with time-varying delays. The developed PIO is equipped with more design freedom leading to better steady-state accuracy compared with the conventional Luenberger observer. The phenomena of randomly occurring gain variations, which are characterized by the Bernoulli distributed random variables with certain probabilities, are taken into consideration in the implementation of the addressed PIO. Attention is focused on the design of a nonfragile PIO such that the error dynamics of the state estimation is exponentially stable in a mean-square sense, and the prescribed H performance index is also achieved. Sufficient conditions for the existence of the desired PIO are established by virtue of the Lyapunov-Krasovskii functional approach and the matrix inequality technique. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed PIO design scheme.
本文针对一类具有时变时滞的离散时间递归神经网络，提出了一种新的比例积分观测器（PIO）设计方法，用于非脆弱 H 状态估计问题。与传统的 Luenberger 观测器相比，所开发的 PIO 具有更多的设计自由度，从而实现更好的稳态精度。在实现所提出的 PIO 时，考虑了增益随机变化的现象，增益随机变化的特征是具有一定概率的伯努利分布随机变量。关注的是设计一种非脆弱的 PIO，使得状态估计的误差动态在均方意义上指数稳定，并达到规定的 H 性能指标。通过 Lyapunov-Krasovskii 泛函方法和矩阵不等式技术，建立了存在所需 PIO 的充分条件。最后，通过一个仿真例子验证了所提出的 PIO 设计方案的有效性。
