The accuracy of the underlying model predictions is crucial for the success of model predictive control (MPC) applications. If the model is unable to accurately analyze the dynamics of the controlled system, the performance and stability guarantees provided by MPC may not be achieved. Learning-based MPC can learn models from data, improving the applicability and reliability of MPC. This study develops a nonlinear sparse variational Bayesian learning based MPC (NSVB-MPC) for nonlinear systems, where the model is learned by the developed NSVB method. Variational inference is used by NSVB-MPC to assess the predictive accuracy and make the necessary corrections to quantify system uncertainty. The suggested approach ensures input-to-state (ISS) and the feasibility of recursive constraints in accordance with the concept of an invariant terminal region. Finally, a PEMFC temperature control model experiment confirms the effectiveness of the NSVB-MPC method.

翻译：底层模型预测的准确性对于模型预测控制（MPC）应用的成功至关重要。如果模型无法准确分析被控系统的动态特性，MPC所提供的性能与稳定性保证可能无法实现。基于学习的MPC能够从数据中学习模型，从而提升MPC的适用性与可靠性。本研究针对非线性系统提出了一种基于非线性稀疏变分贝叶斯学习的MPC（NSVB-MPC），其中模型通过所提出的NSVB方法进行学习。NSVB-MPC利用变分推断评估预测精度，并进行必要的修正以量化系统不确定性。所提出的方法基于不变终端域的概念，确保了输入到状态稳定性（ISS）和递归约束的可行性。最后，通过质子交换膜燃料电池（PEMFC）温度控制模型实验验证了NSVB-MPC方法的有效性。