发表机构
University of Sheffield; ITMO University（谢菲尔德大学; ITMO大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究证明，在广泛线性系统中，最短实验序列（精确状态$mn+1$步，噪声状态$m(n+1)$步）可达到最佳实验误差容限的固定比例，但缓慢驱动系统需$1/h$量级持续时间才能恢复该比例。
AI 中文摘要
在广泛类别的线性系统中，最短实验几乎与最佳可能实验一样有效。对于$n$个状态和$m$个输入，支持所有可控系统鲁棒数据驱动稳定的最短输入序列，在状态精确情况下为$mn+1$步，在状态含噪声情况下为$m(n+1)$步。我们证明，当谱半径有界且谱在单位圆附近良好分离时，这些序列能够容忍由任何实验（即使是完全了解系统并允许使用任意有限持续时间的实验）所达到误差水平的固定比例。这种常数因子比较对于缓慢驱动的系统可能失效。对于$A=I+hG$且可控深度$\nu\ge2$的情况，短实验会损失$h^{\nu-1}$量级的因子，而恢复最优容差的固定比例所需的持续时间量级为$1/h$，且该持续时间既是必要的也是充分的。
英文摘要
On broad classes of linear systems, the shortest experiments are almost as good as the best possible ones. For $n$ states and $m$ inputs, the shortest input sequences that support robust data-driven stabilization of every controllable plant have $mn+1$ steps with exact states and $m(n+1)$ with noisy states. We show that, when the spectral radius is bounded and the spectrum is well separated near the unit circle, these sequences tolerate a fixed fraction of the error level achievable by any experiment, even one designed with full plant knowledge and allowed to use any finite duration. This constant-factor comparison can fail for slowly actuated systems. For $A=I+hG$ with controllability depth $ν\ge2$, short experiments lose a factor of order $h^{ν-1}$, and duration of order $1/h$ is both necessary and sufficient to recover a fixed fraction of the optimal tolerance.
Comments12 pages, 1 table. Submitted to IEEE Transactions on Automatic Control
