发表机构
University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种自调节激励律，使探测激励渐近消失且不损失参数收敛性，通过标量指数权衡协方差衰减速率与激励保留量，数值结果验证了该方法的有效性。
AI 中文摘要
递推辨识中的参数收敛需要持续激励，而持续激励通常由探测信号实现，若无限保留该信号会降低性能。仅用一步预测误差调节探测振幅是不够的，因为小的预测误差并不意味着参数收敛。本文提出一种自调节激励律，其将探测振幅与相关协方差矩阵成比例缩放，使激励仅以估计器自身对剩余参数不确定性的度量所允许的速度消失。核心思路是，为保持参数收敛，激励振幅的衰减速度必须慢于协方差度量（本文中为协方差矩阵的最大特征值）。在该激励律下，激励振幅与协方差度量被证明会共同收敛至零，同时参数估计收敛至真实参数，且整个过程中激励的消失速度慢于协方差度量。该律中的一个标量指数可在协方差衰减速率与保留的激励量之间进行权衡，数值结果证实了这两种特性。
英文摘要
Parameter convergence in recursive identification requires persistent excitation, which is typically enforced with a probing signal that degrades performance if retained indefinitely. Regulating the probing amplitude with the one-step prediction error is insufficient, since a small prediction error does not imply parameter convergence. This paper proposes a self-regulating excitation law that scales the probing amplitude with the associated covariance matrix, so that the excitation vanishes only as fast as the estimator's own measure of remaining parameter uncertainty allows. The key idea is that the excitation amplitude must decay more slowly than the covariance measure, the largest eigenvalue of the covariance matrix in this work, for parameter convergence to be preserved. Under the proposed excitation law, the excitation amplitude and the covariance measure are shown to jointly converge to zero while the parameter estimate converges to the true parameter, with the excitation vanishing more slowly than the covariance measure throughout. A scalar exponent in the law trades the rate of covariance decay against the amount of excitation retained. Numerical results confirm both properties.
