用高斯过程学习不确定系统，实现鲁棒自适应控制。
A robust and adaptive MPC formulation for Gaussian process models
- 基于收缩度量构建高斯过程的鲁棒预测，融入模型预测控制框架。
- 在有界干扰下保证约束满足与状态收敛，概率高于95%。
- 适合复杂非线性系统在线学习与实时控制，如四旋翼飞行器。
本文提出一种针对受有界干扰和未建模非线性影响的不确定非线性系统的鲁棒自适应模型预测控制（MPC）框架。采用高斯过程（GPs）基于噪声测量数据学习不确定动力学，包括系统运行期间采集的数据。关键贡献是利用收缩度量推导出高斯过程模型的鲁棒预测，并将其集成到MPC中。所提设计保证了递归可行性、鲁棒约束满足以及以高概率收敛至参考状态。通过一个受难以建模地面效应影响的平面四旋翼飞行器的数值例子，验证了该方法在鲁棒预测和在线学习方面带来的显著性能提升。
原文摘要 · Abstract (English)
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.
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