Research of Mapping Element Space Method for Uncertain Lurie System Stability Diagnosis

基于相空间递归网络的鲁里叶系统稳定度量

School of Astronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received: 10 September 2018

Abstract

A new diagnosis method of Lurie system stability by using Chaotic time series data was proposed in order to solve stability analysis of flight control system with fault and uncertain. Firstly, the reasons for the instability of the nonlinear system of Ruri leaf was analyzed by using the small gain theory and linear matrix inequalities in the robust control theory. And the stability conditions of Rui leaf system under the condition of uncertainty and failure were proved theoretically. In order to quantify the stability of nonlinear systems in complex Ruri leaves, based on the theory of phase space reconstruction, the nonlinear Ruri system with continuous discrete characteristics was converted into an approximate time discrete equation, mapping it to a low dimensional primitive space, by introducing Q Gauss function into Kernel function, the generalization ability of neural networks are enhanced, realizing the stability analysis method based on the characteristic of primitive migration, which is suitable for various fault and uncertainty conditions, and the relative quantized stability norm can be given. The simulation shows that the present method can effectively solve the stability analysis and determination of flight control system under various factors.

摘要

针对考虑故障、不确定等特性的飞行控制系统稳定性的分析问题，提出了一种基于混沌时间序列数据分析的鲁里叶系统稳定度预测度量方法。首先采用鲁棒控制理论中的小增益理论和线性矩阵不等式，分析了导致鲁里叶非线性系统失稳的多种诱因，在理论上证明了鲁里叶系统在不确定和故障情况下的稳定条件。为了量化分析复杂鲁里叶非线性系统的稳定性，基于相空间重构理论将包含连续离散特性的非线性鲁里叶系统等价转换为近似时间离散方程，将其映射至低维的基元空间中，通过在核函数中引入q高斯函数，更好地增强了神经网络的泛化能力，实现了基于基元迁移特性的稳定性分析方法，适用于多种故障与不确定条件，并可给出相关的量化稳定范数。最终的仿真表明了所提出的方法可有效解决多种因素下的飞行控制系统稳定性分析判定。