From Product Hilbert Spaces to the Generalized Koopman Operator and the Nonlinear Fundamental Lemma

1. 1Derive the generalized Koopman operator using basis functions expansion in a product Hilbert space
2. 2Construct the product Hilbert space as the tensor product between the Hilbert spaces of the state and input
3. 3Apply the nonlinear fundamental lemma to develop data-driven control methods for nonlinear systems
4. 4Evaluate the effectiveness of the proposed solution on various nonlinear systems

This research benefits control systems engineers and AI researchers working on nonlinear systems, as it provides a new framework for data-driven control methods

💡 The generalized Koopman operator can be derived using basis functions expansion in a product Hilbert space

🤖 Novel solution to generalize Koopman operator for nonlinear systems! 📈