  We propose a data-driven method for controlling the frequency and convergence
rate of black-box nonlinear dynamical systems based on the Koopman operator
theory. With the proposed method, a policy network is trained such that the
eigenvalues of a Koopman operator of controlled dynamics are close to the
target eigenvalues. The policy network consists of a neural network to find a
Koopman invariant subspace, and a pole placement module to adjust the
eigenvalues of the Koopman operator. Since the policy network is
differentiable, we can train it in an end-to-end fashion using reinforcement
learning. We demonstrate that the proposed method achieves better performance
than model-free reinforcement learning and model-based control with system
identification.
