In data-driven control, a central question is how to handle noisy data. In this work, we consider the problem of designing a stabilizing controller for an unknown linear system using only a finite set of noisy data collected from the system. For this problem, many recent works have considered a disturbance model based on energy-type bounds. Here, we consider an alternative more natural model where the disturbance obeys instantaneous bounds. In this case, the existing approaches, which would convert instantaneous bounds into energy-type bounds, can be overly conservative. In contrast, without any conversion step, simple arguments based on the S-procedure lead to a very effective controller design through a convex program. Specifically, the feasible set of the latter design problem is always larger, and the set of system matrices consistent with data is always smaller and decreases significantly with the number of data points. These findings and some computational aspects are examined in a number of numerical examples.

在数据驱动控制中，一个核心问题是如何处理嘈杂的数据。在这项工作中，我们考虑仅使用从系统收集的有限噪声数据集为未知线性系统设计稳定控制器的问题。对于这个问题，最近的许多工作都考虑了基于能量类型界限的扰动模型。在这里，我们考虑另一种更自然的模型，其中扰动服从瞬时界限。在这种情况下，将瞬时边界转换为能量类型边界的现有方法可能过于保守。相比之下，没有任何转换步骤，基于 S 过程的简单参数通过凸程序导致非常有效的控制器设计。具体来说，后面的设计问题的可行集总是更大，并且与数据一致的系统矩阵集总是较小，并且随着数据点的数量而显着减少。这些发现和一些计算方面在许多数值例子中得到了检验。