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This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear statespace model. To the best of our knowledge, our method is the first to utilize Koopman eigenfunctions as lifting functions for EDMD-based methods. We demonstrate the performance of the framework in state prediction and closed loop trajectory tracking of a simulated cart pole system. Our method is able to significantly improve the controller performance while relying on linear control methods to do nonlinear control.

This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear dynamics by learning the eigenvalues and eigenfunctions of the associated Koopman operator. We then exploit the learned Koopman eigenfunctions to learn a lifted linear statespace model. To the best of our knowledge, our method is the first to utilize Koopman eigenfunctions as lifting functions for EDMD-based methods. We demonstrate the performance of the framework in state prediction and closed loop trajectory tracking of a simulated cart pole system. Our method is able to significantly improve the controller performance while relying on linear control methods to do nonlinear control.

Control barrier functions (CBFs) are a powerful tool to guarantee safety of autonomous systems, yet they rely on the computation of control invariant sets, which is notoriously difficult. A backup strategy employs an implicit control invariant set computed by forward integrating the system dynamics. However, this integration is prohibitively expensive for high dimensional systems, and inaccurate in the presence of unmodelled dynamics. We propose to learn discrete-time Koopman operators of the closed-loop dynamics under a backup strategy. This approach replaces forward integration by a simple matrix multiplication, which can mostly be computed offline. We also derive an error bound on the unmodeled dynamics in order to robustify the CBF controller. Our approach extends to multi-agent systems, and we demonstrate the method on collision avoidance for wheeled robots and quadrotors.

This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the Koopman operator approach to nonlinear dynamical systems analysis, which models the flow of observables in a function space, rather than a flow in a state space. Practically, this method estimates a nonlinear diffeomorphism that lifts the dynamics to a higher dimensional space where they are linear. Efficient Model Predictive Control methods can then be applied to the lifted model. This approach allows for real time implementation in on-board hardware, with rigorous incorporation of both input and state constraints during learning. We demonstrate the method in a real-time implementation of fast multirotor landing, where the nonlinear ground effect is learned and used to improve landing speed and quality.