Generalized Forgetting Recursive Least Squares: Stability and Robustness Guarantees

被引：8

作者：

Lai, Brian ^{[1
]}

Bernstein, Dennis S. ^{[1
]}

机构：

[1] Univ Michigan, Dept Aerosp Engn, Ann Arbor, MI 48109 USA

来源：

IEEE TRANSACTIONS ON AUTOMATIC CONTROL | 2024年 / 69卷 / 11期

关键词：

Asymptotic stability; Noise; Robustness; Cost function; Sufficient conditions; Symmetric matrices; Parameter estimation; Identification; recursive least squares (RLS); robustness; stability analysis; errors in variables; ERRORS-IN-VARIABLES; EXPONENTIAL CONVERGENCE; ALGORITHM; PERSISTENCY; SYSTEMS;

D O I：

10.1109/TAC.2024.3394351

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This work presents generalized forgetting recursive least squares (GF-RLS), a generalization of RLS that encompasses many extensions of RLS as special cases. First, sufficient conditions are presented for the 1) Lyapunov stability, 2) uniform Lyapunov stability, 3) global asymptotic stability, and 4) global uniform exponential stability of parameter estimation error in GF-RLS when estimating fixed parameters without noise. Second, robustness guarantees are derived for the estimation of time-varying parameters in the presence of measurement noise and regressor noise. These robustness guarantees are presented in terms of global uniform ultimate boundedness of the parameter estimation error. A specialization of this result gives a bound to the asymptotic bias of least squares estimators in the errors-in-variables problem. Lastly, a survey is presented to show how GF-RLS can be used to analyze various extensions of RLS from literature.

引用

页码：7646 / 7661

页数：16

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