Scenario-based model predictive control (MPC) methods introduce recourse into optimal control, and can thus reduce the conservativeness inherent to open-loop robust MPC. However, the uncertainty scenarios are often generated offline using worst-case uncertainty bounds quantified a priori, limiting the potential gains in control performance. This paper presents a learning-based multistage MPC (msMPC) for systems with hard-to-model dynamics and time-varying plant-model mismatch. Gaussian Processes (GP) are used to learn state- and input-dependent plant-model mismatch in real-time and accordingly adapt the scenario tree online. Due to the increased computational complexity associated with incorporating the GP predictions into the optimal control problem, the learning-based msMPC (LB-msMPC) law is approximated by a deep neural network (DNN) that is cheap-to-evaluate online and has a small memory footprint, which makes it suitable for embedded applications. In addition, we present a novel algorithm for training the DNN-based controller that uses a GP description of the plant-model mismatch to generate closed-loop simulation data, which ensures the LB-msMPC law is evaluated in regions of the state space most relevant to closed-loop operation. The proposed LB-msMPC strategy is demonstrated on a cold atmospheric plasma jet with applications in (bio)materials processing. The simulation results indicate the promise of the approximate LB-msMPC strategy for control of hard-to-model systems with fast dynamics on millisecond timescales.

基于场景的模型预测控制（MPC）方法将资源引入最优控制，因此可以减少开环鲁棒MPC固有的保守性。但是，不确定性场景通常是使用先验量化的最坏情况不确定性边界离线生成的，限制了控制性能的潜在收益。本文针对具有难以建模的动力学和时变工厂模型不匹配的系统，提出了一种基于学习的多级MPC（msMPC）。高斯过程（GP）用于实时了解状态和输入相关的工厂模型不匹配，并相应地在线调整方案树。由于将GP预测合并到最佳控制问题中而导致计算复杂性的提高，基于学习的msMPC（LB-msMPC）规律由可在网上进行廉价评估的深层神经网络（DNN）近似。较小的内存占用空间，使其适合嵌入式应用程序。此外，我们提出了一种用于训练基于DNN的控制器的新颖算法，该算法使用工厂模型不匹配的GP描述来生成闭环仿真数据，这样可以确保在与闭环操作最相关的状态空间区域中评估LB-msMPC律。拟议的LB-msMPC策略在冷大气等离子流中得到证明，并应用于（生物）材料加工中。仿真结果表明，近似的LB-msMPC策略有望在毫秒级时标上以快速动态控制难于建模的系统。