基于粗粒度辨识的鲁棒控制非渐近性分析
Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification
摘要：
这项工作探讨了之间的权衡所需的样本个数，以准确地建立模型的动力系统和性能退化，在各种控制目标，由于粗糙的近似。特别是，我们表明，简单的模型可以很容易地从输入/输出数据，并足以实现各种控制目标。我们从一个稳定的线性定常系统，足以保证相应的有限冲激响应近似接近真实的系统中的$\mathcal{H}_\infty$ -范数的噪声输入/输出样本的数量上的界限。我们证明，这些要求低于那些在现有技术中得到的，旨在准确地识别动态模型。我们还探讨了不同的物理输入约束，如功率约束，如何影响样本的复杂性。最后，我们展示了我们的分析如何适合在既定的框架内的鲁棒控制，通过演示如何控制器设计的近似系统可证明满足真正的系统的性能目标。
英文摘要：
This work explores the trade-off between the number of samples required to accurately build models of dynamical systems and the degradation of performance in various control objectives due to a coarse approximation. In particular, we show that simple models can be easily fit from input/output data and are sufficient for achieving various control objectives. We derive bounds on the number of noisy input/output samples from a stable linear time-invariant system that are sufficient to guarantee that the corresponding finite impulse response approximation is close to the true system in the $\mathcal{H}_\infty$-norm. We demonstrate that these demands are lower than those derived in prior art which aimed to accurately identify dynamical models. We also explore how different physical input constraints, such as power constraints, affect the sample complexity. Finally, we show how our analysis fits within the established framework of robust control, by demonstrating how a controller designed for an approximate system provably meets performance objectives on the true system.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
