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：本文针对闭环可观测随机线性系统，提出了一种基于符号扰动和（SPS）有限样本系统辨识方法的推广方案，用于其状态空间形式的辨识。该方法基于矩阵变量回归和工具变量方法理论，构建状态空间矩阵的无分布置信区域。研究涵盖了直接辨识与间接辨识两种途径，并证明了所构建置信区域的精确性及强一致性。此外，本文提出了一种计算高效的新型椭球外逼近算法，用于置信区域的近似。该算法将问题转化为半定优化问题，其约束条件数量相较于向量化后直接应用椭球外逼近方法降低了数量级。通过一系列数值实验，本文还从经验角度验证了该方法的有效性。