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：本文提出了信号扰动和（SPS）有限样本系统辨识方法的一种推广形式，用于辨识状态空间形式的闭环可观测随机线性系统。该方案基于矩阵变量回归理论与仪器变量方法，构建了状态空间矩阵的无分布置信域。本文研究了直接辨识与间接辨识两种途径，并证明了所构建置信域的精确性与强一致性。此外，提出了一种计算高效的椭球体外近似算法用于生成置信域。该新构造方法导出一个半定优化问题，其约束数量相比于向量化后直接应用椭球体外近似算法降低了数量级。通过一系列数值实验，该方法的有效性也得到了实证验证。