An Improved Approach for Implementing Dynamic Mode Decomposition with Control

Abstract

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’s 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.