An Optimization Approach to Select Koopman Observables for Data-Based Modeling Using Dynamic Mode Decomposition with Control

作     者：Marti-Coll, Amanda Rodriguez-Ramos, Adrian Llanes-Santiago, Orestes 

作者机构：Univ Tecnol Habana Jose Antonio Echeverria Dept Automat & Comp CUJAE Calle 114 11901 Marianao 19390 Cuba 

出 版 物：《PROCESSES》 (Process.)

年 卷 期：2025年第13卷第1期

页      面：284-284页

核心收录：

基　　金：Ministry of Science, Technology and Environment from Cuba National Program of Science and Technology on Automation [PN223LH004-ARIA] 

主　　题：optimization process digital twins Koopman observables dynamical mode decomposition with control evolutive algorithms 

摘      要：The advent and evolution of Industry 4.0 have been driven by technologies such as the Industrial Internet of Things, Big Data, and Cloud Computing. Within this framework, digital twins have gained significant popularity and are now employed across a wide range of industries and processes. A crucial step in developing a digital twin is deriving the system model, for which numerous methods are available. Among these, the Koopman operator and Dynamic Mode Decomposition with control have demonstrated their effectiveness and are widely recognized in the scientific community. This paper proposes a procedure for the automatic selection of Koopman observables by solving an optimization problem. The objective is to identify the minimal set of observables, belonging to a predefined dictionary, that minimize the error between actual process observations and predictions made by the estimated linear model-a key requirement for digital twin development. To tackle the optimization challenge, any algorithm available in the literature can be utilized. In this paper, the evolutive algorithms, including Genetic Algorithm and Differential Evolution Algorithm, are applied to evaluate the proposed approach in a benchmark problem. In both cases, the algorithms obtained the minimum set of observable functions from the dictionary used that achieve the lowest error obtained between the real process and the model, confirming the validity of the proposed method.