Nuclear norm regularised dynamic mode decomposition

• DOI: 10.1049/iet-spr.2015.0352
• Publication Date: 2016-03-09T11:09:55Z
• Authors: Shaobo Wang; Xiangyun Qing
• Keywords: Dynamic Mode Decomposition; Matrix norm

As a data-driven, equation-free decomposition method, the DMD can characterise dynamic behaviour of non-linear system by using modes and eigenvalues. However, all current provable algorithms suffer from separate procedure for obtaining determining number modes. In this study, authors propose nuclear norm regularised (NNR-DMD) algorithm that produces low-dimensional spatio-temporal A regularisation term is added to optimisation problem standard prompting sparsity projected Split Bregman method applied solve convex, but non-smooth problem. Several numerical examples demonstrate potential proposed NNR-DMD algorithm: (i) it identify in which each them possesses single temporal frequency; (ii) reconstruction errors based on sparse be reduced when compares with sparsity-promoting penalising l1 -norm vector amplitudes; (iii) obtain coherent structures coherency identification generators an interconnected power system.