时变参数辨识梯度算法稳定性分析

研究用于时变参数辨识的梯度算法稳定性问题.基于随机过程有界性判据对时变参数辨识梯度算法进行了稳定性分析,给出了梯度算法稳定的充分条件.指出在待辨识参数变化率有界,观测噪声是零均值白噪声,且系统满足持续激励条件的情况下,梯度算法参数选择满足一定条件时,能够确保参数辨识误差的有界性.上述研究与以往工作的不同之处在于稳定性证明过程中仅要求待辨识参数的变化率是有界的,而不要求参数变化率是零均值白噪声.

Stability Analysis of Time-Varying Parameter Identification Gradient Algorithm

The stability of a gradient algorithm for time-varying parameter identification is studied in this paper.The stability of the time-varying parameter identification gradient algorithm is analyzed by using the stochastic process boundedness criterion.The sufficient conditions to ensure the stability of the gradient algorithm are demonstrated.It is shown that if the rate of variation of the parameter to be identified is bounded,and the measurement noise is zero-mean white noise,under the persistent excitation condition,the identification error given by the properly designed gradient algorithm is bounded in the sence of mean square.This analysis is different from prior works in that it is not necessary to assume that the parameter variation is the zero-mean white noise in the proof of the theory.