针对不稳定非线性系统，给出单轨迹数据下参数估计的非渐近误差保证。
Non-Asymptotic Bounds for Closed-Loop Identification of Sub-Exponentially Growing Nonlinear Stochastic Systems
- 基于带探索输入的闭环数据，结合子指数增长假设进行参数估计。
- 在状态空间特定区域，可获得高概率误差上界，全空间则全域有效。
- 适用于现有方法难以覆盖的非线性不稳定系统分析，适合控制理论研究者。
我们研究离散时间、不稳定、闭环非线性随机系统的单轨迹数据最小二乘参数估计问题。考虑具有线性参数化不确定性和独立同分布过程噪声的系统，其反馈控制策略受有意探索输入扰动。假设开环动态满足特定的子指数输入-状态增长性质，且状态空间某一区域能产生信息数据，我们在该区域状态演化时建立了参数估计误差的非渐近保证。若整个状态空间均具信息性，则误差的高概率上界对所有时刻成立。文中提供了示例，表明该结果可拓展至现有工作无法覆盖的分析场景。
原文摘要 · Abstract (English)
We investigate the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems. Specifically, we consider nonlinear systems with linearly parametrised uncertainty and additive i.i.d. process noise, in feedback with a control policy that is intentionally perturbed by an exploratory input. Assuming the open-loop dynamics satisfy a particular sub-exponential input-to-state growth property, and a region of the state space produces informative data, we establish non-asymptotic guarantees on the estimation error at times when the state trajectory evolves in this region. If the whole state space is informative, high-probability guarantees on the error hold for all times. Examples are provided where our results are useful for analysis beyond existing works.
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