Accelerated proximal gradient method for systems with unknown structure using Volterra series

Chen, Jing; Gan, Min; Cheng, Lianyuan; Zhu, Quanmin

Abstract

Systems with unknown structures widely exist in engineering practices. In this paper, a Volterra series is applied to approximate the dynamics of systems. Due to the special structure of the Volterra model, the approximated model has a high order and some redundant terms. A regularised term is introduced to pick out these redundant terms, and then a proximal gradient method is provided to estimate the unknown parameters of the Volterra model. Furthermore, an accelerated technique is proposed to increase the convergence rates. The advantages of this algorithm are as follows: (1) can pick out the redundant terms without any prior knowledge of the model; (2) has fast convergence rates; and (3) is robust to the step-size. The effectiveness of the proposed algorithm is further substantiated through a simulation example.

• Journal Article Type: Article
• Acceptance Date: Nov 20, 2024
• Online Publication Date: Nov 28, 2024
• Deposit Date: Jan 16, 2025
• Publicly Available Date: Nov 29, 2025
• Journal: International Journal of Control
• Print ISSN: 0020-7179
• Electronic ISSN: 1366-5820
• Publisher: Taylor & Francis
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1080/00207179.2024.2433984
• Public URL: https://uwe-repository.worktribe.com/output/13528365