The paper suggests a generalization of the Sign-Perturbed Sums (SPS) finite sample system identification method for the identification of closed-loop observable stochastic linear systems in state-space form. The solution builds on the theory of matrix-variate regression and instrumental variable methods to construct distribution-free confidence regions for the state-space matrices. Both direct and indirect identification are studied, and the exactness as well as the strong consistency of the construction are proved. Furthermore, a new, computationally efficient ellipsoidal outer-approximation algorithm for the confidence regions is proposed. The new construction results in a semidefinite optimization problem which has an order-of-magnitude smaller number of constraints, as if one applied the ellipsoidal outer-approximation after vectorization. The effectiveness of the approach is also demonstrated empirically via a series of numerical experiments.

翻译：本文提出了一种符号扰动和（SPS）有限样本系统辨识方法的推广，用于辨识状态空间形式下的闭环可观测随机线性系统。该解决方案基于矩阵变量回归理论和工具变量方法，为状态空间矩阵构建无分布置信域。研究涵盖了直接辨识与间接辨识，并证明了所构建置信域的精确性与强一致性。此外，提出了一种新的计算高效置信域椭球外逼近算法。新构建方法产生一个半定优化问题，其约束数量级显著减少，相当于在向量化后应用椭球外逼近。通过一系列数值实验，实证验证了该方法的有效性。