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Nonlinear model predictive control (MPC) is a flexible and increasinglypopular framework used to synthesize feedback control strategies that cansatisfy both state and control input constraints. In this framework, anoptimization problem, subjected to a set of dynamics constraints characterizedby a nonlinear dynamics model, is solved at each time step. Despite itsversatility, the performance of nonlinear MPC often depends on the accuracy ofthe dynamics model. In this work, we leverage deep learning tools, namelyknowledge-based neural ordinary differential equations (KNODE) and deepensembles, to improve the prediction accuracy of this model. In particular, welearn an ensemble of KNODE models, which we refer to as the KNODE ensemble, toobtain an accurate prediction of the true system dynamics. This learned modelis then integrated into a novel learning-enhanced nonlinear MPC framework. Weprovide sufficient conditions that guarantees asymptotic stability of theclosed-loop system and show that these conditions can be implemented inpractice. We show that the KNODE ensemble provides more accurate predictionsand illustrate the efficacy and closed-loop performance of the proposednonlinear MPC framework using two case studies.

Learning-enhanced Nonlinear Model Predictive Control using Knowledge-based Neural Ordinary Differential Equations and Deep Ensembles