Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification
Non-Asymptotic Analysis of Robust Control from Coarse-Grained Identification
复制标题
粗粒度辨识的鲁棒控制非渐近分析
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
B. Recht
中科院分区：
文献类型：
--
作者：
Stephen Tu;Ross Boczar;A. Packard;B. Recht
这项工作探讨了准确建立动态系统模型所需的样本数量与由于粗略近似而导致的各种控制目标的性能下降之间的权衡。特别是，我们证明了简单的模型可以很容易地从输入/输出数据中拟合，并且足以实现各种控制目标。我们从一个稳定的线性时不变系统中得到了噪声输入/输出样本个数的界，这些界足以保证相应的有限脉冲响应近似在$\数学{H}_\inty$-范数下接近真实系统。我们证明，这些要求比现有技术中旨在准确识别动力学模型的要求要低。我们还探索了不同的物理输入限制，如功率限制，如何影响样本复杂性。最后，我们通过演示为近似系统设计的控制器如何在真实系统上证明满足性能目标，来说明我们的分析如何符合所建立的鲁棒控制框架。
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.