一类基于神经网络的非线性时延系统的稳定性分析和控制

Stability Analysis and Control for Nonlinear Time-Delay System Based on Neural Network

针对一类有参数摄动和时延的非线性不确定性系统．提出了一种稳定性分析方法。控制方案将鲁棒控制和神经网络控制结合起来．首先由线性矩阵不等式(LMI)设计了参考模型即系统线性部分的鲁棒控制器,然后用神经网络来消除系统建模不确定非线性部分。稳定性分析中综合了参数摄动、时延和神经网络权值．合理地选择Lyapunov函数证明了误差闭环系统的稳定性．

A kind of stability method is presented for a class of uncertain nonlinear system with perturbation and time delay. The control scheme combines the robust control with the neural network control. Firstly the reference model--the linear part of the system of the robust controller is designed by linear matrix inequality（LMI）. And then, the modeling uncertain nonlinear part is compensated by the neural network. The stability analysis synthesizes the parameter perturbation, the time delay and the neural network weight. The stability of the error closed loop system is proved by choosing a rational lyapunov function. Simulation results demonstrate that the control scheme is effective.