论文标题
关于$ \ Mathcal {l} _2 $ - gain的数据驱动推断的样本复杂性
On the Sample Complexity of Data-Driven Inference of the $\mathcal{L}_2$-gain
论文作者
论文摘要
最近，数据驱动的控制已成为广泛的研究领域。对于非线性系统数据驱动控制的一些基于大数据的方法，尝试使用经典的输入输出技术来设计控制器的系统，仅知道有限数量的（输入输出）样本。这些方法着重于使用给定数据来计算$ \ Mathcal {l} _2 $ - gain或从有限输入输入数据中的被动性短缺上，从而适用了small增益定理或被无源系统的反馈定理。关于这些方法的一个问题询问了它们的样本复杂性，即需要多少个输入输出样本来获得操作员规范的近似值或被动性短缺。我们表明，估计系统运算符规范所需的样品数量大致与近似操作员规范中系统所需的样本数量相同。
Lately, data-driven control has become a widespread area of research. A few recent big-data based approaches for data-driven control of nonlinear systems try to use classical input-output techniques to design controllers for systems for which only a finite number of (input-output) samples are known. These methods focus on using the given data to compute bounds on the $\mathcal{L}_2$-gain or on the shortage of passivity from finite input-output data, allowing for the application of the small gain theorem or the feedback theorem for passive systems. One question regarding these methods asks about their sample complexity, namely how many input-output samples are needed to get an approximation of the operator norm or of the shortage of passivity. We show that the number of samples needed to estimate the operator norm of a system is roughly the same as the number of samples required to approximate the system in the operator norm.
