Finite-Data Performance Guarantees for the Output-Feedback Control of an Unknown System
Ross Boczar Nikolai Matni Benjamin Recht
Abstract
As the systems we control become more complex, first-principle modeling becomes either impossible or intractable, motivating the use of machine learning techniques for the control of systems with continuous action spaces. As impressive as the empirical success of these methods have been, strong theoretical guarantees of performance, safety, or robustness are few and far between. This paper takes a step towards such providing such guarantees by establishing finite-data performance guarantees for the robust output-feedback control of an unknown FIR SISO system. In particular, we introduce the “Coarse-ID control” pipeline, which is composed of a system identification step followed by a robust controller synthesis procedure, and analyze its end-to-end performance, providing quantitative bounds on the performance degradation suffered due to model uncertainty as a function of the number of experiments run to identify the system. We conclude with numerical examples demonstrating the effectiveness of our method.
中文速览
用数据驱动方法控制未知系统时，人们往往缺乏严格的性能与安全保证，而这篇论文正是要填补这一空白。作者提出了"粗粒度-ID控制"（Coarse-ID Control）流程：先用有限次实验对未知的单输入单输出（SISO）有限脉冲响应（FIR）系统做系统辨识，再利用系统级综合（System-Level Synthesis，SLS）框架设计鲁棒输出反馈控制器，并对整个流程进行端到端分析。核心结论是：当用 $m$ 次实验、噪声方差为 $\sigma^2$ 来估计系统时，合成控制器的性能损失（与真实最优控制器相比）以 $O\!\left(\sqrt{\sigma^2 r / m}\right)$ 的速率收敛到零，给出了明确的有限样本性能界。这项工作的重要意义在于，它首次将非渐近系统辨识误差界与鲁棒控制综合定量地串联起来，为数据驱动控制在安全关键场景中的应用奠定了理论基础。
原文 arXiv:1803.09186;中英对照 + 大白话阅读 https://aha.fim.ai/paper/1803.09186v2