  In this work, we consider the problem of deriving and incorporating accurate
dynamic models for model predictive control (MPC) with an application to
quadrotor control. MPC relies on precise dynamic models to achieve the desired
closed-loop performance. However, the presence of uncertainties in complex
systems and the environments they operate in poses a challenge in obtaining
sufficiently accurate representations of the system dynamics. In this work, we
make use of a deep learning tool, knowledge-based neural ordinary differential
equations (KNODE), to augment a model obtained from first principles. The
resulting hybrid model encompasses both a nominal first-principle model and a
neural network learnt from simulated or real-world experimental data. Using a
quadrotor, we benchmark our hybrid model against a state-of-the-art Gaussian
Process (GP) model and show that the hybrid model provides more accurate
predictions of the quadrotor dynamics and is able to generalize beyond the
training data. To improve closed-loop performance, the hybrid model is
integrated into a novel MPC framework, known as KNODE-MPC. Results show that
the integrated framework achieves 60.2% improvement in simulations and more
than 21% in physical experiments, in terms of trajectory tracking performance.
