Nonlinear model predictive control (MPC) is a flexible and increasingly popular framework used to synthesize feedback control strategies that can satisfy both state and control input constraints. In this framework, an optimization problem, subjected to a set of dynamics constraints characterized by a nonlinear dynamics model, is solved at each time step. Despite its versatility, the performance of nonlinear MPC often depends on the accuracy of the dynamics model. In this work, we leverage deep learning tools, namely knowledge-based neural ordinary differential equations (KNODE) and deep ensembles, to improve the prediction accuracy of this model. In particular, we learn an ensemble of KNODE models, which we refer to as the KNODE ensemble, to obtain an accurate prediction of the true system dynamics. This learned model is then integrated into a novel learning-enhanced nonlinear MPC framework. We provide sufficient conditions that guarantees asymptotic stability of the closed-loop system and show that these conditions can be implemented in practice. We show that the KNODE ensemble provides more accurate predictions and illustrate the efficacy and closed-loop performance of the proposed nonlinear MPC framework using two case studies.

翻译：非线性模型预测控制(MPC)是一种灵活且日益流行的框架，用于合成能够同时满足状态和控制输入约束的反馈控制策略。在该框架中，每个时间步需求解一个受非线性动力学模型约束的优化问题。尽管非线性MPC具有通用性，但其性能往往依赖于动力学模型的精度。本研究利用深度学习工具——即基于知识的神经常微分方程(KNODE)与深度集成——提升该模型的预测精度。具体而言，我们学习一个KNODE模型集成（称为KNODE集成），以获得系统真实动力学的精确预测。随后将该学习模型集成至一种新型学习增强型非线性MPC框架中。我们给出了保证闭环系统渐近稳定性的充分条件，并证明这些条件在实践中可实现。通过两个案例研究，我们展示了KNODE集成可提供更精确的预测，并验证了所提非线性MPC框架的有效性与闭环性能。