Delayed Standard Neural Network Models for Control Systems
Delayed Standard Neural Network Models for Control Systems
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DOI：
10.1109/tnn.2007.894084
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发表时间：
2007-09
影响因子：
--
通讯作者：
Meiqin Liu
中科院分区：
文献类型：
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作者：
Meiqin Liu
为了方便地分析递归神经网络(RNN)的稳定性，并成功地综合非线性系统的控制器，类似于线性鲁棒控制理论中的标称模型，提出了一种新的神经网络模型，称为延迟标准神经网络模型(DSNNM)，它是线性动态系统和有界静态时滞(或非时滞)非线性算子的互联。通过将多种不同的Lyapunov泛函与S过程相结合，得到了连续时间DSNNM和离散时间DSNNMS全局渐近稳定和全局指数稳定的一些有用的判据，其条件表示为线性矩阵不等式(LMI)。在稳定性分析的基础上，设计了具有输入输出的DSNNM的状态反馈控制律，以使闭环系统镇定。大多数具有(或不具有)时滞的RNN和神经控制非线性系统都可以转化为DSNNM进行稳定性分析或镇定综合。本文将DSNNMS应用于具有和不具有时滞的连续时间和离散时间RNN的稳定性分析，以及混沌神经网络系统和离散时间非线性系统的状态反馈控制器的综合。结果表明，DSNNM使得RNN的稳定性条件易于验证，为非线性系统控制器的综合提供了一种新的思路。
In order to conveniently analyze the stability of recurrent neural networks (RNNs) and successfully synthesize the controllers for nonlinear systems, similar to the nominal model in linear robust control theory, the novel neural network model, named delayed standard neural network model (DSNNM) is presented, which is the interconnection of a linear dynamic system and a bounded static delayed (or nondelayed) nonlinear operator. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability for the continuous-time DSNNMs (CDSNNMs) and discrete-time DSNNMs (DDSNNMs) are derived, whose conditions are formulated as linear matrix inequalities (LMIs). Based on the stability analysis, some state-feedback control laws for the DSNNM with input and output are designed to stabilize the closed-loop systems. Most RNNs and neurocontrol nonlinear systems with (or without) time delays can be transformed into the DSNNMs to be stability-analyzed or stabilization-synthesized in a unified way. In this paper, the DSNNMs are applied to analyzing the stability of the continuous-time and discrete-time RNNs with or without time delays, and synthesizing the state-feedback controllers for the chaotic neural-network-system and discrete-time nonlinear system. It turns out that the DSNNM makes the stability conditions of the RNNs easily verified, and provides a new idea for the synthesis of the controllers for the nonlinear systems.