{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,22]],"date-time":"2025-11-22T10:34:21Z","timestamp":1763807661260,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,8]],"date-time":"2023-10-08T00:00:00Z","timestamp":1696723200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Dynamic Mode Decomposition with Control is a powerful technique for analyzing and modeling complex dynamical systems under the influence of external control inputs. In this paper, we propose a novel approach to implement this technique that offers computational advantages over the existing method. The proposed scheme uses singular value decomposition of a lower order matrix and requires fewer matrix multiplications when determining corresponding approximation matrices. Moreover, the matrix of dynamic modes also has a simpler structure than the corresponding matrix in the standard approach. To demonstrate the efficacy of the proposed implementation, we applied it to a diverse set of numerical examples. The algorithm\u2019s flexibility is demonstrated in tests: accurate modeling of ecological systems like Lotka-Volterra, successful control of chaotic behavior in the Lorenz system and efficient handling of large-scale stable linear systems. This showcased its versatility and efficacy across different dynamical systems.<\/jats:p>","DOI":"10.3390\/computation11100201","type":"journal-article","created":{"date-parts":[[2023,10,9]],"date-time":"2023-10-09T04:56:43Z","timestamp":1696827403000},"page":"201","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["An Improved Approach for Implementing Dynamic Mode Decomposition with Control"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0474-1987","authenticated-orcid":false,"given":"Gyurhan","family":"Nedzhibov","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Informatics, Shumen University, 9700 Shumen, Bulgaria"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1137\/15M1013857","article-title":"Dynamic mode decomposition with control","volume":"15","author":"Proctor","year":"2016","journal-title":"SIAM J. 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