2024/06/01 by Haonan Xu, Yingying Li, Xu, Haonan +1
Engineering · Mathematics · #Advanced Control Systems Optimization #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Fuzzy Systems and Optimization #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2406.00574
openalex publication_date 2024/06/01 · openalex created_date 2024/06/06 · openalex updated_date 2026/07/28
This paper revisits the set membership identification for linear control systems and establishes its convergence rates under relaxed assumptions on (i) the persistent excitation requirement and (ii) the system disturbances. In particular, instead of assuming persistent excitation exactly, this paper adopts the block-martingale small-ball condition enabled by randomly perturbed control policies to establish the convergence rates of SME with high probability. Further, we relax the assumptions on the shape of the bounded disturbance set and the boundary-visiting condition. Our convergence rates hold for disturbances bounded by general convex sets, which bridges the gap between the previous convergence analysis for general convex sets and the existing convergence rate analysis for ℓ_∞ balls. Further, we validate our convergence rates by several numerical experiments. This manuscript contains supplementary content in the Appendix.