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This paper provides a comprehensive introduction to Koopman operator theory, emphasizing its application in creating data-driven surrogate models for complex dynamical systems. By leveraging techniques such as extended dynamic mode decomposition (EDMD) and Koopman model predictive control (MPC), the authors illustrate how these methods can yield finite-dimensional approximations with quantifiable error bounds. The tutorial includes practical simulation studies and source code to facilitate hands-on learning and implementation of the Koopman operator in control systems.
Unlocking the power of Koopman operator theory could revolutionize how we model and control complex dynamical systems with unprecedented accuracy and efficiency.
The Koopman operator has gained considerable attention due to its ability to provide a global linear representation of highly complex dynamical systems. The operator describes nonlinear dynamics in a linear way through the lens of real- or complex-valued observable functions. Recently proposed data-driven techniques, like extended dynamic mode decomposition (EDMD), its kernelized variant, and machine-learning methods, can be used to generate finite-dimensional approximations accompanied by finite-data error bounds. In this tutorial paper, we provide a concise introduction into Koopman operator theory and its use in systems and control. A particular focus is put on data-driven surrogate models, their extension to systems with inputs, and controller design using Koopman operator theory. Moreover, we demonstrate the key techniques, i.e., EDMD and Koopman MPC. To this end, we provide simulation studies including source code on GitHub to enable the interested reader to experience the Koopman operator in systems and control step by step.
