We propose a novel framework for learning linear time-invariant (LTI) models for a class of continuous-time non-autonomous nonlinear dynamics based on a representation of Koopman operators. In general, the operator is infinite-dimensional but, crucially, linear. To utilize it for efficient LTI control, we learn a finite representation of the Koopman operator that is linear in controls while concurrently learning meaningful lifting coordinates. For the latter, we rely on KoopmanizingFlows - a diffeomorphism-based representation of Koopman operators. With such a learned model, we can replace the nonlinear infinite-horizon optimal control problem with quadratic costs to that of a linear quadratic regulator (LQR), facilitating efficacious optimal control for nonlinear systems. The prediction and control efficacy of the proposed method is verified on simulation examples.
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