标题： 一种针对高斯过程模型的鲁棒自适应MPC公式 显示英文标题

标题： A robust and adaptive MPC formulation for Gaussian process models

摘要： 在本文中，我们提出了一种稳健且自适应的模型预测控制（MPC）框架，用于受有界扰动和未建模非线性影响的不确定非线性系统。我们使用高斯过程（GPs）基于噪声测量数据学习不确定动力学，包括在系统运行期间收集的数据。作为主要贡献，我们利用收缩度量为GP模型推导出稳健预测，并将其纳入MPC公式中。所提出的设计保证了递归可行性、鲁棒约束满足性和对参考状态的收敛性，具有很高的概率。我们提供了一个平面四旋翼机的数值示例，该四旋翼机受到难以建模的地面效应影响，这突显了通过所提出的稳健预测方法和在线学习实现的显著改进。 显示英文摘要

摘要： In this paper, we present a robust and adaptive model predictive control (MPC) framework for uncertain nonlinear systems affected by bounded disturbances and unmodeled nonlinearities. We use Gaussian Processes (GPs) to learn the uncertain dynamics based on noisy measurements, including those collected during system operation. As a key contribution, we derive robust predictions for GP models using contraction metrics, which are incorporated in the MPC formulation. The proposed design guarantees recursive feasibility, robust constraint satisfaction and convergence to a reference state, with high probability. We provide a numerical example of a planar quadrotor subject to difficult-to-model ground effects, which highlights significant improvements achieved through the proposed robust prediction method and through online learning.