Finite Sample System Identification: Improved Rates and the Role of Regularization
This paper studies low-order linear system identification via regularized regression. The nuclear norm of the system’s Hankel matrix is added as a regularizer to the least-squares cost function due to the following advantages. The regularized problem is (1) often easier to tune, (2) has lower sample complexity, and (3) returns a Hankel matrix with a clear singular value gap, which robustly recovers a low-order linear system from noisy output observations. Recently, the performance of the unregularized least-squares formulations have been studied statistically in terms of finite sample complexity and recovery errors; however, no results are known for the regularized approach. In this work, we provide a novel statistical analysis of the regularized algorithm. Our analysis leads to new bounds on estimating the impulse response and the Hankel matrix associated with the system while using smaller number of observations than the least-squares estimator.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Learning Linearized Models from Nonlinear Systems with Finite Data
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under …
Learning Linearized Models from Nonlinear Systems under Initialization Constraints with Finite Data
The identification of a linear system model from data has wide applications in control theory. The existing work that provides finite sample guarantees for linear system identification typically uses data from a single l…
Finite Sample Analysis for a Class of Subspace Identification Methods
While subspace identification methods (SIMs) are appealing due to their simple parameterization for MIMO systems and robust numerical realizations, a comprehensive statistical analysis of SIMs remains an open problem, es…
Achieving $\widetilde{O}(1/ε)$ Sample Complexity for Bilinear Systems Identification under Bounded Noises
This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Our analysis considers trajectory-dependent regressors and allows margin…
Finite Sample Analysis of Stochastic System Identification
In this paper, we analyze the finite sample complexity of stochastic system identification using modern tools from machine learning and statistics. An unknown discrete-time linear system evolves over time under Gaussian …
parameter estimationvalid