IEEE Trans Neural Netw Learn Syst. 2018 Apr;29(4):1376-1381. doi: 10.1109/TNNLS.2017.2661862. Epub 2017 Feb 16.
This brief is concerned with the problem of neural state estimation for static neural networks with time-varying delays. Notice that a Luenberger estimator can produce an estimation error irrespective of the neuron state trajectory. This brief provides a method for designing such an estimator for static neural networks with time-varying delays. First, in-depth analysis on a well-used reciprocally convex approach is made, leading to an improved reciprocally convex inequality. Second, the improved reciprocally convex inequality and some integral inequalities are employed to provide a tight upper bound on the time-derivative of some Lyapunov-Krasovskii functional. As a result, a novel bounded real lemma (BRL) for the resultant error system is derived. Third, the BRL is applied to present a method for designing suitable Luenberger estimators in terms of solutions of linear matrix inequalities with two tuning parameters. Finally, it is shown through a numerical example that the proposed method can derive less conservative results than some existing ones.
本简报关注的是时变时滞静态神经网络的神经状态估计问题。请注意，卢恩伯格估计器可以产生与神经元状态轨迹无关的估计误差。本简报为时变时滞静态神经网络设计了这样的估计器。首先，对常用的互凸逼近方法进行了深入分析，得到了改进的互凸不等式。其次，利用改进的互凸不等式和一些积分不等式，对某些李雅普诺夫-克拉索夫斯基泛函的时间导数给出了紧的上界。结果，推导出了新的误差系统有界实引理（BRL）。第三，将 BRL 应用于通过具有两个调整参数的线性矩阵不等式的解来设计合适的卢恩伯格估计器的方法。最后，通过数值例子表明，与一些现有的方法相比，所提出的方法可以得出更保守的结果。
