Robust Data-Driven Control for Systems with Noisy Data

Data-driven stabilization of nonlinear polynomial systems with noisy data

In a recent paper we have shown how to learn controllers for unknown linear systems using finite-sized noisy data by solving linear matrix inequalities. In this note we extend this approach to deal with unknown nonlinear polynomial systems by formulating stability certificates in the form of data-dependent sum of squares programs, whose solution directly provides a stabilizing controller and a Lyapunov function. We then derive variations of this result that lead to more advantageous controller designs. The results also reveal connections to the problem of designing a controller starting from a…

基于噪声数据的高效数据驱动优化

Efficient Data-Driven Optimization with Noisy Data

本文研究测量噪声污染下的数据驱动处方问题，提出具有熵最优传输解释的高效鲁棒公式，并利用Strassen表示结果证明其在多种场景下可求解。

基于算子的数据嵌入：从含噪数据出发的连续时间系统数据驱动控制

Operator-based data embedding for data-driven control of continuous-time systems from noisy data

该研究针对含噪数据提出基于算子的数据嵌入方法，刻画与数据一致的系统集合，推导数据可辨识性条件并构造反馈增益，得到连续时间信号重构误差上界，用于连续时间系统的数据驱动控制。

噪声数据库中基于局部凸重构的物理约束数据驱动方法

A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database

物理约束数据驱动计算是一种新兴的混合方法，它将通用物理定律与实验数据的数据驱动模型相结合，用于科学计算。提出了一种新的数据驱动的模拟方法，结合局部凸重构，称为局部凸数据驱动（LCDD）计算，以提高精度和鲁棒性的数据驱动计算中的数据集的噪声和离群值。在该方法中，对于通过物理模拟获得的给定状态，通过将该状态投影到基于最近的实验数据重构的相关联的局部凸流形上来寻求相应的最优实验解。这种局部数据结构的学习过程对噪声数据不太敏感，因此产生更好的准确性。惩罚松弛也被引入到重铸的非负最小二乘的上下文中，可以有效地解决局部学习求解器。再生核近似与稳定的节点积分的物理流形的解决方案，以允许减少应力应变数据在离散点的LCDD学习求解器的有效性增强。由于固有的流形学习特性，LCDD在实际工程应用中相对稀疏的高维数据集上表现良好。数值试验表明，LCDD在处理噪声数据库时比标准的最小距离数据驱动格式提高了近一个数量级的精度，并且在局部应力应变关系为线性时达到了线性精度。

Controller design for robust invariance from noisy data

For an unknown linear system, starting from noisy open-loop input-state data collected during a finite-length experiment, we directly design a linear feedback controller that guarantees robust invariance of a given polyhedral set of the state in the presence of disturbances. The main result is a necessary and sufficient condition for the existence of such a controller, and amounts to the solution of a linear program. The benefits of large and rich data sets for the solution of the problem are discussed. A numerical example about a simplified platoon of two vehicles illustrates the method.

使用含噪测量的直接数据驱动控制

Direct Data Driven Control Using Noisy Measurements

针对未知动态且状态含噪的LQR问题，提出仅用单条含噪轨迹、基于LMI与SDP直接综合控制器的框架，保证均方稳定与最优性能。

LyAm：面向噪声环境中稳定学习的鲁棒非凸优化

LyAm: Robust Non-Convex Optimization for Stable Learning in Noisy Environments

针对深度神经网络训练中噪声梯度与不稳定收敛的问题，提出结合Adam与Lyapunov稳定性机制的新型优化器LyAm，理论证明其非凸收敛性，并在CIFAR等数据集上验证了其优于现有方法的准确率与稳定性。

噪声数据是因祸得福吗？一个分布鲁棒优化视角

Is Noisy Data a Blessing in Disguise? A Distributionally Robust Optimization Perspective

本文提出通过Wasserstein球逆像在潜在分布上构建DRO模糊集，证明噪声数据可降低保守性、提升最优值并改善公平资源分配。

On data-driven control: informativity of noisy input-output data with cross-covariance bounds

In this paper we develop new data informativity based controller synthesis methods that extend existing frameworks in two relevant directions: a more general noise characterization in terms of cross-covariance bounds and informativity conditions for control based on input-output data. Previous works have derived necessary and sufficient informativity conditions for noisy input-state data with quadratic noise bounds via an S-procedure. Although these bounds do not capture cross-covariance bounds in general, we show that the S-procedure is still applicable for obtaining non-conservative conditio…

使用总变差距离处理含噪声数据的离散不确定性分布鲁棒优化

Distributionally-Robust Optimization with Noisy Data for Discrete Uncertainties Using Total Variation Distance

本文研究从含噪声数据推断分布的随机规划，提出基于总变差距离构建模糊集的分布鲁棒优化方法，证明其渐近一致性并转化为可处理的凸优化问题，适用于大规模随机问题。

探索带噪标签下上下文学习的鲁棒性

Exploring the Robustness of In-Context Learning with Noisy Labels

本文系统评估了Transformer在上下文学习中对示例标签噪声的鲁棒性，并发现向训练集引入噪声作为数据增强可进一步提升推理时的抗噪能力，为理解ICL韧性提供了新见解。