Input Design for Kernel-Based System Identification From the Viewpoint of Frequency Response

This paper discusses a method for designing input sequences for kernel-based system identification methods from the frequency perspective. The goal of this paper is to minimize the posterior uncertainty of the spectrum over the frequency band of the interest. A tractable criterion for this purpose is proposed, which is related to the so-called Bayesian A-optimality. An online algorithm that gives a suboptimal input for this criterion is proposed. Moreover, it is shown that the optimal solution can be obtained in an offline manner under a certain condition. The effectiveness of these methods is demonstrated through numerical simulations.