Exact LTI Koopman models for nonlinear control systems require affine linear dynamics under controllability and coordinate inclusion assumptions.
On the existence of Koopman linear embeddings for controlled nonlinear systems
5 Pith papers cite this work. Polarity classification is still indexing.
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Presents necessary differential geometric conditions on vector fields for Koopman linearizability of control-affine systems, shown sufficient for weaker versions and necessary and sufficient with one extra condition for controllable linear targets.
Nonlinear discrete-time systems are shown to admit exact bilinear representations via separate RKHS lifts of state and input, with stabilization posed as optimization over conditional probability measures.
A method is proposed to design data-driven output-feedback controllers for nonlinear systems with provable exponential stability guarantees using only input-output measurements via Koopman-based bilinear surrogate models on extended states.
Tutorial on Koopman operator theory, data-driven methods such as EDMD, and their use in controller design for nonlinear systems with provided simulations and code.
citing papers explorer
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Limitations of LTI Koopman Modeling for Nonlinear Control Systems
Exact LTI Koopman models for nonlinear control systems require affine linear dynamics under controllability and coordinate inclusion assumptions.
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Differential Geometric Conditions for Koopman Linearizability of Control-Affine Systems
Presents necessary differential geometric conditions on vector fields for Koopman linearizability of control-affine systems, shown sufficient for weaker versions and necessary and sufficient with one extra condition for controllable linear targets.
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Koopman Modeling and Stabilization of Discrete-Time Nonlinear Control Systems: Bilinearity on a Reproducing Kernel Hilbert Space
Nonlinear discrete-time systems are shown to admit exact bilinear representations via separate RKHS lifts of state and input, with stabilization posed as optimization over conditional probability measures.
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Koopman meets input-output data: Data-driven output-feedback control of nonlinear systems with closed-loop guarantees
A method is proposed to design data-driven output-feedback controllers for nonlinear systems with provable exponential stability guarantees using only input-output measurements via Koopman-based bilinear surrogate models on extended states.
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Koopman operator theory: fundamentals, control, and applications
Tutorial on Koopman operator theory, data-driven methods such as EDMD, and their use in controller design for nonlinear systems with provided simulations and code.