An approach to stability criteria of neural-network control systems
An approach to stability criteria of neural-network control systems
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DOI：
10.1109/72.501721
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发表时间：
1996-05
影响因子：
--
通讯作者：
Kazuo Tanaka
中科院分区：
文献类型：
--
作者：
Kazuo Tanaka
利用Lyapunov方法讨论了基于神经网络的控制系统的稳定性问题。首先，指出神经网络系统的动力学可以用线性微分包含(LDI)的非线性系统来表示。其次，给出了这类非线性系统的稳定性条件，并将其应用于单神经网络系统和反馈神经网络控制系统的稳定性分析。在此基础上，通过引入顶点和最小表示的新概念，提出了一种用图形表示非线性系统参数位置的参数区域表示方法。从这些概念出发，导出了一个重要的定理，该定理有助于有效地求出一个Lyapunov函数。用PR表示法给出了单神经网络系统的稳定性判据。最后，分析了由一个神经网络和一个神经网络控制器组成的反馈神经网络控制系统的稳定性。
This paper discusses stability of neural network (NN)-based control systems using Lyapunov approach. First, it is pointed out that the dynamics of NN systems can be represented by a class of nonlinear systems treated as linear differential inclusions (LDI). Next, stability conditions for the class of nonlinear systems are derived and applied to the stability analysis of single NN systems and feedback NN control systems. Furthermore, a method of parameter region (PR) representation, which graphically shows the location of parameters of nonlinear systems, is proposed by introducing new concepts of vertex point and minimum representation. From these concepts, an important theorem, which is useful for effectively finding a Lyapunov function, is derived. Stability criteria of single NN systems are illustrated in terms of PR representation. Finally, stability of feedback NN control systems, which consist of a plant represented by an NN and an NN controller, is analyzed.