The focus of this paper is on linear system identification in the setting where it is known that the underlying partially-observed linear dynamical system lies within a finite collection of known candidate models. We first consider the problem of identification from a given trajectory, which in this setting reduces to identifying the index of the true model with high probability. We characterize the finite-time sample complexity of this problem by leveraging recent advances in the non-asymptotic analysis of linear least-square methods in the literature. In comparison to the earlier results that assume no prior knowledge of the system, our approach takes advantage of the smaller hypothesis class and leads to the design of a learner with a dimension-free sample complexity bound. Next, we consider the switching control of linear systems, where there is a candidate controller for each of the candidate models and data is collected through interaction of the system with a collection of potentially destabilizing controllers. We develop a dimension-dependent criterion that can detect those destabilizing controllers in finite time. By leveraging these results, we propose a data-driven switching strategy that identifies the unknown parameters of the underlying system. We then provide a non-asymptotic analysis of its performance and discuss its implications on the classical method of estimator-based supervisory control.

在已知部分观测的线性动态系统属于已知候选模型的有限集合的情况下，本文关注线性系统识别问题。我们首先考虑了给定轨迹的识别问题，利用线性最小二乘方法的最新非渐近分析进展来表征这个问题的有限时间样本复杂性，并设计了一个维度无关样本复杂性界的学习器。接下来，我们考虑了线性系统的切换控制问题，其中每个候选模型都有一个候选控制器，并通过系统与一组潜在的破坏性控制器的交互来收集数据，我们开发了一个维度相关的准则来在有限时间内检测这些破坏性控制器。我们利用这些结果提出了一个数据驱动的切换策略来识别潜在系统的未知参数，并对其性能进行了非渐近分析，并讨论了其对基于估计的监督控制方法的影响。

线性切换控制中的非渐进标识的最小二乘方法