Exact LTI Koopman models for nonlinear control systems require affine linear dynamics under controllability and coordinate inclusion assumptions.
Generalizing Koopman theory to allow for inputs and control
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Bilinear input modulation in coupled SSMs improves both memory and bilinear computation, with seq-BIM and p-BIM outperforming gated modulation and uniquely benefiting from larger state dimensions on pendulum and NARMA-10 tasks.
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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.