标题： 学习增强控制：竞争MPC中的自适应置信学习 显示英文标题

标题： Learning-Augmented Control: Adaptively Confidence Learning for Competitive MPC

摘要： 我们引入了学习增强控制（LAC），这是一种将不可信的机器学习预测整合到约束非线性动力系统控制中的方法。 LAC旨在实现“两种世界最佳”的保证，即当预测准确时达到近似最优性能，当预测不准确时保持鲁棒和安全的性能。 我们方法的核心是一种延迟置信度学习过程，该过程在线优化一个置信度参数，自适应地在机器学习预测和名义预测之间进行平衡。 我们在标准MPC正则性假设下，为一般的非线性系统建立了形式化的竞争比边界。 对于线性二次情况，我们推导了一个可证明紧致的竞争比边界，从而明确了这种学习增强方法的基本极限。 LAC的有效性在数值研究中得到验证，其中它在对抗性预测误差下保持稳定并优于标准方法。 显示英文摘要

摘要： We introduce Learning-Augmented Control (LAC), an approach that integrates untrusted machine learning predictions into the control of constrained, nonlinear dynamical systems. LAC is designed to achieve the "best-of-both-worlds" guarantees, i.e, near-optimal performance when predictions are accurate, and robust, safe performance when they are not. The core of our approach is a delayed confidence learning procedure that optimizes a confidence parameter online, adaptively balancing between ML and nominal predictions. We establish formal competitive ratio bounds for general nonlinear systems under standard MPC regularity assumptions. For the linear quadratic case, we derive a competitive ratio bound that is provably tight, thereby characterizing the fundamental limits of this learning-augmented approach. The effectiveness of LAC is demonstrated in numerical studies, where it maintains stability and outperforms standard methods under adversarial prediction errors.