2022/08/02 by Mohammad R. Khosravi, Mohammad Khosravi, Khosravi, Mohammad · 5 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #FOS: Electrical engineering #Model Reduction and Neural Networks #Neural Networks and Applications #Numerical methods in inverse problems #Signal Processing (eess.SP) #Systems and Control (eess.SY) #cs.SY #eess.SP #eess.SY #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2208.01681
arxiv created 2022/08/02 · openalex publication_date 2022/08/02 · arxiv updated 2022/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, the problem of learning Koopman operator of a discrete-time autonomous system is considered. The learning problem is formulated as a constrained regularized empirical loss minimization in the infinite-dimensional space of linear operators. We show that under certain but general conditions, a representer theorem holds for the learning problem. This allows reformulating the problem in a finite-dimensional space without any approximation and loss of precision. Following this, we consider various cases of regularization and constraints in the learning problem, including the operator norm, the Frobenius norm, rank, nuclear norm, and stability. Subsequently, we derive the corresponding finite-dimensional problem. Furthermore, we discuss the connection between the proposed formulation and the extended dynamic mode decomposition. Finally, we provide an illustrative numerical example.