Koopman Operator

The Koopman operator provides a framework for linearizing the dynamics of nonlinear systems, enabling the application of linear systems theory to complex problems. Current research focuses on developing data-driven methods, often employing neural networks (like autoencoders and Kolmogorov-Arnold networks) and algorithms such as Dynamic Mode Decomposition (DMD), to learn Koopman operators from observational data and improve model accuracy and efficiency. This approach is proving valuable in diverse fields, including robotics, control systems, and fluid dynamics, by facilitating more accurate predictions, robust control design, and enhanced understanding of complex system behavior. The ability to represent nonlinear systems in a linear framework offers significant advantages for analysis, prediction, and control.