Introduction to Koopman Operator in Modeling and Control of Dynamic Systems

This paper briefly introduces the Koopman operator framework in the modeling and control of dynamic systems. The paper reviews the theoretical foundations of the Koopman operator, presenting implications for modeling and control in engineering systems. We describe the extended dynamic mode decomposition method to approximate the Koopman operator in a finite-dimensional space. We then show how an autoencoder is obtained for the approximated Koopman operator and analyze the uncertainty quantification. Numerical simulation reveals the validity of the proposed method. We also briefly review the interdisciplinary significance of the physics-informed Koopman operator and its potential to revolutionize the analysis and control of complex dynamic systems across various domains.