发表机构
University of Sheffield; ITMO University（谢菲尔德大学; 伊托莫大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对标量离散时间系统，精确确定了有界实验在镇定验证中可容忍的噪声上限，区分个体可镇定性、公共增益镇定与公共二次证书，并给出长时域极限及多维推广，为未知对象设计提供鲁棒性基准。
AI 中文摘要
一个有界实验在仍能确定被控对象可被镇定之前，能容忍多少未知的过程噪声？我们针对具有有界输入、精确状态测量以及扰动能量预算与实验长度成正比的标量离散时间系统回答了这个问题。我们区分了每个一致模型的个体可镇定性、通过一个公共增益实现的镇定以及一个公共二次证书。我们确定了每种漂移下的精确噪声上限。后两个要求一致；个体可镇定性通常能容忍更多噪声。有界周期输入接近这些上限，而对抗性扰动则阻止其达到。我们还确定了长时域极限。对于不稳定被控对象，短实验可以在噪声水平下确立个体可镇定性，而任何足够长的实验在该噪声水平下都会失败。同样的障碍为具有实特征值的多维系统提供了上界。输入设计可以利用被控对象知识，但认证仅使用记录的数据和噪声界限。因此，这些结果为未知被控对象设计提供了基本的鲁棒性基准。
英文摘要
How much unknown process noise can a bounded experiment tolerate while still establishing that the plant can be stabilized? We answer this question for scalar discrete-time systems with bounded inputs, exact state measurements, and a disturbance-energy budget proportional to the experiment length. We distinguish individual stabilizability of every consistent model, stabilization by one common gain, and a common quadratic certificate. We determine their exact noise ceilings for every drift. The last two requirements coincide; individual stabilizability generally tolerates more noise. Bounded periodic inputs approach the ceilings, while adversarial disturbances prevent their attainment. We also determine the long-horizon limits. For unstable plants, a short experiment can establish individual stabilizability at noise levels where every sufficiently long experiment fails. The same obstruction yields upper bounds for multidimensional systems with real eigenvalues. Input design may use plant knowledge, but certification uses only the recorded data and noise bound. The results therefore provide fundamental robustness benchmarks for unknown-plant designs.
Comments6 pages, 1 figure. Submitted to the American Control Conference (ACC)
