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We propose a data-driven method for controlling the frequency and convergencerate of black-box nonlinear dynamical systems based on the Koopman operatortheory. With the proposed method, a policy network is trained such that theeigenvalues of a Koopman operator of controlled dynamics are close to thetarget eigenvalues. The policy network consists of a neural network to find aKoopman invariant subspace, and a pole placement module to adjust theeigenvalues of the Koopman operator. Since the policy network isdifferentiable, we can train it in an end-to-end fashion using reinforcementlearning. We demonstrate that the proposed method achieves better performancethan model-free reinforcement learning and model-based control with systemidentification.

Data-driven End-to-end Learning of Pole Placement Control for Nonlinear Dynamics via Koopman Invariant Subspaces