Recursive Least Squares with Fading Regularization for Finite-Time Convergence without Persistent Excitation
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.
Code (0)
등록된 구현이 없습니다.
Tasks
parameter estimationSimilar Papers 제목 키워드 기반
Regularization-Induced Bias and Consistency in Recursive Least Squares
Within the context of recursive least squares (RLS) parameter estimation, the goal of the present paper is to study the effect of regularization-induced bias on the transient and asymptotic accuracy of the parameter esti…
parameter estimationregressionConvergence of Recursive Least Squares Based Input/Output System Identification with Model Order Mismatch
Discrete-time input/output models, also called infinite impulse response (IIR) models or autoregressive moving average (ARMA) models, are useful for online identification as they can be efficiently updated using recursiv…
Adaptive Kalman Filtering Developed from Recursive Least Squares Forgetting Algorithms
Recursive least squares (RLS) is derived as the recursive minimizer of the least-squares cost function. Moreover, it is well known that RLS is a special case of the Kalman filter. This work presents the Kalman filter lea…
State EstimationRegularization-free estimation in trace regression with symmetric positive semidefinite matrices
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regula…
compressed sensingMatrix CompletionQuantum State TomographyregressionRecursive Least Squares Policy Control with Echo State Network
The echo state network (ESN) is a special type of recurrent neural networks for processing the time-series dataset. However, limited by the strong correlation among sequential samples of the agent, ESN-based policy contr…
Time SeriesTime Series Analysis