Unifying Model-Based and Neural Network Feedforward: Physics-Guided Neural Networks with Linear Autoregressive Dynamics

Unknown nonlinear dynamics often limit the tracking performance of feedforward control. The aim of this paper is to develop a feedforward control framework that can compensate these unknown nonlinear dynamics using universal function approximators. The feedforward controller is parametrized as a parallel combination of a physics-based model and a neural network, where both share the same linear autoregressive (AR) dynamics. This parametrization allows for efficient output-error optimization through Sanathanan-Koerner (SK) iterations. Within each SK-iteration, the output of the neural network is penalized in the subspace of the physics-based model through orthogonal projection-based regularization, such that the neural network captures only the unmodelled dynamics, resulting in interpretable models.