This paper discusses the problem of system identification when frequency domain side-information is available. We mainly consider the case where the side-information is provided as the ${\mathcal{H}}_{\infty }$-norm of the system being bounded by a given scalar. This framework allows considering different forms of frequency domain side-information, such as the dissipativity of the system. We propose a nonparametric identification approach for estimating the impulse response of the system under the given side-information. The estimation problem is formulated as a constrained optimization in a stable reproducing kernel Hilbert space, where suitable constraints are considered for incorporating the desired frequency domain features. The resulting optimization has an infinite-dimensional feasible set with an infinite number of constraints. We show that this problem is a well-defined convex program with a unique solution. We propose a heuristic that tightly approximates this unique solution. The proposed approach is equivalent to solving a finite-dimensional convex quadratically constrained quadratic program. The efficiency of the discussed method is verified by several numerical examples.

本文讨论了频域边信息可用时的系统辨识问题。我们主要考虑提供辅助信息作为${\mathcal{H}}_{\infty }$- 系统受给定标量限制的范数。该框架允许考虑不同形式的频域辅助信息，例如系统的耗散性。我们提出了一种非参数识别方法，用于在给定的边信息下估计系统的脉冲响应。估计问题被表述为稳定再现内核 Hilbert 空间中的约束优化，其中考虑了合适的约束以合并所需的频域特征。生成的优化具有无限维可行集和无限数量的约束。我们表明这个问题是一个定义明确的凸规划，具有唯一的解决方案。我们提出了一种启发式方法，可以紧密地近似于这种独特的解决方案。所提出的方法等效于求解有限维凸二次约束二次规划。通过几个数值例子验证了所讨论方法的有效性。