IEEE Trans Neural Netw Learn Syst. 2015 Dec;26(12):2987-98. doi: 10.1109/TNNLS.2015.2399331. Epub 2015 Feb 27.
This paper investigates the H∞ state estimation problem for a class of discrete-time nonlinear systems of the neural network type with random time-varying delays and multiple missing measurements. These nonlinear systems include recurrent neural networks, complex network systems, Lur'e systems, and so on which can be described by a unified model consisting of a linear dynamic system and a static nonlinear operator. The missing phenomenon commonly existing in measurements is assumed to occur randomly by introducing mutually individual random variables satisfying certain kind of probability distribution. Throughout this paper, first a Luenberger-like estimator based on the imperfect output data is constructed to obtain the immeasurable system states. Then, by virtue of Lyapunov stability theory and stochastic method, the H∞ performance of the estimation error dynamical system (augmented system) is analyzed. Based on the analysis, the H∞ estimator gains are deduced such that the augmented system is globally mean square stable. In this paper, both the variation range and distribution probability of the time delay are incorporated into the control laws, which allows us to not only have more accurate models of the real physical systems, but also obtain less conservative results. Finally, three illustrative examples are provided to validate the proposed control laws.
本文研究了一类具有随机时变时滞和多重缺失测量的神经网络型离散时间非线性系统的 H∞状态估计问题。这些非线性系统包括递归神经网络、复杂网络系统、Lur'e 系统等，可以用一个由线性动态系统和静态非线性算子组成的统一模型来描述。假设通过引入满足某种概率分布的相互独立的随机变量，测量中常见的缺失现象随机发生。在整篇论文中，首先基于不完美的输出数据构建了一个类似于 Luenberger 的估计器，以获得不可测量的系统状态。然后，利用 Lyapunov 稳定性理论和随机方法，分析了估计误差动态系统（增广系统）的 H∞性能。在此基础上，推导出了 H∞估计器增益，使得增广系统全局均方稳定。在本文中，时滞的变化范围和分布概率都被纳入到控制律中，这不仅使我们能够拥有更精确的实际物理系统模型，而且还能得到更保守的结果。最后，通过三个实例验证了所提出的控制律。
