递推阻尼最小二乘法的收敛性与稳定性

Convergence and Stability of Recursive Damped Least Square Algorithm

递推最小二乘法是参数辨识中最常用的方法,但容易产生参数爆发现象· 因此对一种更稳定的辨识方法———递推阻尼最小二乘法进行了收敛特性的分析· 在使用算法之前先归一化测量向量,结果表明,参数化距离收敛于一个零均值随机变量,并且在持续激励条件下,适应增益矩阵的条件数有界· 参数化距离的方差有界·

The recursive least square is widely used in parameter identification. But it is easy to bring about the phenomena of parameters burst_off. A convergence analysis of a more stable identification algorithm_recursive damped least square is proposed. This is done by normalizing the measurement vector entering into the identification algorithm. It is shown that the parametric distance converges to a zero mean random variable. It is also shown that under persistent excitation condition, the condition number of the adaptation gain matrix is bounded, and the variance of the parametric distance is bounded.