  The identification of a mathematical dynamics model is a crucial step in the
designing process of a controller. However, it is often very difficult to
identify the system's governing equations, especially in complex environments
that combine physical laws of different disciplines. In this paper, we present
a new approach that allows identifying an ordinary differential equation by
means of a physics-informed machine learning algorithm. Our method introduces a
special neural network that allows exploiting prior human knowledge to a
certain degree and extends it autonomously, so that the resulting differential
equations describe the system as accurately as possible. We validate the method
on a Duffing oscillator with simulation data and, additionally, on a cascaded
tank example with real-world data. Subsequently, we use the developed algorithm
in a model-based reinforcement learning framework by alternately identifying
and controlling a system to a target state. We test the performance by
swinging-up an inverted pendulum on a cart.
