We consider the problem of least squares parameter estimation from single-trajectory data for discrete-time, unstable, closed-loop nonlinear stochastic systems, with linearly parameterised uncertainty. Assuming a region of the state space produces informative data, and the system is sub-exponentially unstable, we establish non-asymptotic guarantees on the estimation error at times where 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, but existing results are not.

翻译：本文研究离散时间、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，系统不确定性具有线性参数化形式。假设状态空间的某个区域能产生信息性数据，且系统具有次指数不稳定性，我们建立了当状态轨迹在该区域内演化时估计误差的非渐近保证。若整个状态空间均具有信息性，则误差的高概率保证对所有时间成立。我们提供了若干实例，表明现有方法无法处理而本文结果具有分析价值的情形。