  In this work, we consider the task of improving the accuracy of dynamic
models for model predictive control (MPC) in an online setting. Although
prediction models can be learned and applied to model-based controllers, these
models are often learned offline. In this offline setting, training data is
first collected and a prediction model is learned through an elaborated
training procedure. However, since the model is learned offline, it does not
adapt to disturbances or model errors observed during deployment. To improve
the adaptiveness of the model and the controller, we propose an online dynamics
learning framework that continually improves the accuracy of the dynamic model
during deployment. We adopt knowledge-based neural ordinary differential
equations (KNODE) as the dynamic models, and use techniques inspired by
transfer learning to continually improve the model accuracy. We demonstrate the
efficacy of our framework with a quadrotor, and verify the framework in both
simulations and physical experiments. Results show that our approach can
account for disturbances that are possibly time-varying, while maintaining good
trajectory tracking performance.
