Greedy Search Method for Separable Nonlinear Models Using Stage Aitken Gradient Descent and Least Squares Algorithms
- Resource Type
- Periodical
- Authors
- Chen, J.; Mao, Y.; Gan, M.; Wang, D.; Zhu, Q.
- Source
- IEEE Transactions on Automatic Control IEEE Trans. Automat. Contr. Automatic Control, IEEE Transactions on. 68(8):5044-5051 Aug, 2023
- Subject
- Signal Processing and Analysis
Convergence
Mathematical models
Computational modeling
Cost function
Eigenvalues and eigenfunctions
Iterative algorithms
Search methods
Aitken acceleration technique
convergence rate
hierarchical identification algorithm
parameter estimation
separable nonlinear model
- Language
- ISSN
- 0018-9286
1558-2523
2334-3303
Aitken gradient descent (AGD) algorithm takes some advantages over the standard gradient descent and Newton methods: 1) can achieve at least quadratic convergence in general; 2) does not require the Hessian matrix inversion; 3) has less computational efforts. When using the AGD method for a considered model, the iterative function should be unchanging during all the iterations. This article proposes a hierarchical AGD algorithm for separable nonlinear models based on stage greedy method. The linear parameters are estimated using the least squares algorithm, and the nonlinear parameters are updated based on the AGD algorithm. Since the iterative function is changing at each iteration, a stage AGD algorithm is introduced. The convergence properties and simulation examples show effectiveness of the proposed algorithm.