2025/04/26 by Uday Kiran Reddy Tadipatri, Benjamin D. Haeffele, Tadipatri, Uday Kiran Reddy +7 · 1 citation
Engineering · Mathematics · #Advanced Optimization Algorithms Research #Control Systems and Identification #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2504.18791
openalex publication_date 2025/04/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Low-order linear System IDentification (SysID) addresses the challenge of estimating the parameters of a linear dynamical system from finite samples of observations and control inputs with minimal state representation. Traditional approaches often utilize Hankel-rank minimization, which relies on convex relaxations that can require numerous, costly singular value decompositions (SVDs) to optimize. In this work, we propose two nonconvex reformulations to tackle low-order SysID (i) Burer-Monterio (BM) factorization of the Hankel matrix for efficient nuclear norm minimization, and (ii) optimizing directly over system parameters for real, diagonalizable systems with an atomic norm style decomposition. These reformulations circumvent the need for repeated heavy SVD computations, significantly improving computational efficiency. Moreover, we prove that optimizing directly over the system parameters yields lower statistical error rates, and lower sample complexities that do not scale linearly with trajectory length like in Hankel-nuclear norm minimization. Additionally, while our proposed formulations are nonconvex, we provide theoretical guarantees of achieving global optimality in polynomial time. Finally, we demonstrate algorithms that solve these nonconvex programs and validate our theoretical claims on synthetic data.