Robust Model Predictive Control With Neural Ordinary Differential Equations for Nonlinear Systems

ABSTRACT This article presents a model predictive control (MPC) strategy that leverages neural ordinary differential equations (NODEs) to address the persistent issue of model mismatch in nonlinear systems. A residual model based on NODEs is employed to capture the differences between the actual system dynamics and conventional models. Simultaneously, an approximate model with an uncertainty upper bound, derived from first principles, is introduced. These two models are integrated into a learning‐based MPC framework, effectively decoupling system safety and performance, leading to more reliable control. To enhance model and controller adaptability, we propose an online dynamic learning framework that continuously refines the accuracy of the dynamic model. Compared to traditional learning‐based MPC, the proposed algorithm significantly reduces memory usage. Furthermore, using the theory of invariant sets, we establish the recursive feasibility and stability of the algorithm. The method's effectiveness is demonstrated through addressing nonlinear problems involving modeling errors and stochastic disturbances.