Optimal Set-Membership Smoothing

• 成果类型: Article
• 署名作者: Li, Yudong; Cong, Yirui; Zhou, Xiangyun; Dong, Jiuxiang
• 署名单位: Northeastern University - China; Northeastern University - China; National University of Defense Technology - China; Australian National University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3632158
• 发表日期: 2026
• 关键词: state; tracking

摘要

This article studies the optimal set-membership smoothing (SMSing) problem for the system with bounded noises. By adopting the mathematical concept of uncertain variables, an optimal SMSing framework is established for the first time. This optimal framework reveals the principles of SMSing and the relationship between set-membership filtering and smoothing. Based on the design principles, we put forward two SMSing algorithms: one for linear systems with zonotopic constrained uncertainties, where the solution is given in a closed form, and the other for a class of nonlinear systems. Numerical simulations corroborate the effectiveness of our theoretical results.