Goal-Oriented Input Design for Kernel-Based System Identification

This paper discusses an input design problem for the Kernel-Based system identification, which estimates the impulse response of the system in the Bayesian estimation framework. In particular, we focus on quantities described by real-valued linear functionals of the impulse response, such as DC gain, step response in the transient, and frequency response in the specified frequency. The goal of this paper is to design the input for identification such that the weighted sum of the errors of these functionals is minimized. An algorithm which generates the locally optimal input sequence is proposed, and also some special cases where the locally optimal input is available in a closed-form are shown. Numerical simulation is given to illustrate the effectiveness of the proposed method.