面向无持续激励下有限时间收敛的带渐消正则化递推最小二乘
Recursive Least Squares with Fading Regularization for Finite-Time Convergence without Persistent Excitation
AI总结：
提出带时变渐消正则化的R1FR-RLS算法，可在无弱持续激励条件下实现参数估计误差收敛，正则化有限时间归零时误差亦有限时间收敛，且复杂度与经典RLS相同。
摘要：
本文将递推最小二乘（RLS）扩展为包含时变正则化的形式。这一扩展为实时更新最小二乘正则化项提供了灵活性。现有关于恒定正则化的结果表明，当且仅当回归因子满足弱持续激励条件时，RLS的参数估计误差动态才会全局吸引至零。本研究表明，通过将经典RLS扩展为包含一个收敛至零的时变（渐消）正则化项，参数估计误差动态可在无需弱持续激励的情况下全局吸引至零。此外，若渐消正则化项在有限时间内收敛至零，则参数估计误差也会在有限时间内收敛至零。最后，我们提出了秩一渐消正则化（R1FR）RLS，这是一种带渐消正则化且正则化项收敛至零的时变正则化算法，其计算复杂度与经典RLS相同。文中给出了数值算例，以验证理论保证并展示R1FR-RLS如何防止过度正则化。
英文摘要：
This paper extends recursive least squares (RLS) to include time-varying regularization. This extension provides flexibility for updating the least squares regularization term in real time. Existing results with constant regularization imply that the parameter-estimation error dynamics of RLS are globally attractive to zero if and only the regressor is weakly persistently exciting. This work shows that, by extending classical RLS to include a time-varying (fading) regularization term that converges to zero, the parameter-estimation error dynamics are globally attractive to zero without weakly persistent excitation. Moreover, if the fading regularization term converges to zero in finite time, then the parameter estimation error also converges to zero in finite time. Finally, we propose rank-1 fading regularization (R1FR) RLS, a time-varying regularization algorithm with fading regularization that converges to zero, and which runs in the same computational complexity as classical RLS. Numerical examples are presented to validate theoretical guarantees and to show how R1FR-RLS can protect against over-regularization.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
