Optimal Set-Membership Smoothing

2024/10/13 by Yudong Li, Yirui Cong, Li, Yudong +5
Decision Sciences · #Auction Theory and Applications #FOS: Electrical engineering #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2410.09857

openalex publication_date 2024/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This article studies the Set-Membership Smoothing (SMSing) problem for non-stochastic Hidden Markov Models. 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.

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