Nonlinear MPC with RNN-Based Neural ODEs Trained on Trajectory Tracking Demonstrations

This paper presents a trajectory-tracking control framework that integrates a data-driven error dynamics model-learned from demonstration data via a Neural Ordinary Differential Equation-Recurrent Neural Network (NODE-RNN) architecture-with a nonlinear model predictive control (NMPC) scheme. Conventional NMPC relies on fixed analytical error models that are inflexible to environmental variations, vulnerable to disturbances, and sensitive to model uncertainty. To address these limitations, we integrate a recurrent neural network (RNN) that preserves temporal information in its hidden states and captures nonlinear dynamics with a Neural ODE, which models the continuous-time error derivatives from those hidden states via Euler integration. The resulting learned model replaces the conventional analytical error dynamics within the NMPC predictive function. Through simulation studies on demonstration datasets with diverse distributions, the proposed NODE-RNN-NMPC framework is shown to converge to the desired trajectory more rapidly and precisely than conventional baseline controllers.