Stochastic input design problems for the frequency response in Bayesian identification

Abstract

Recently, the research of identification input design for Bayesian methods has been actively investigated. Either the problem is formulated as a non-convex problem with difficulty in solving or relaxed as a convex problem with a price of some conservativeness. In this contribution, a new minimum power input design problem is formulated by viewing the input as a stochastic process. We seek the minimum energy input with variance constraints over a frequency band. By exploiting the generalized Kalman-Yakubovich-Popov lemma, the stochastic consideration facilitates the input design problem to be presented as a convex problem whose decision variables are a finite number of autocorrelation coefficients. We obtain the autocorrelation coefficients of the desired stochastic input signal by solving the convex problem and extend them by the maximum entropy extension. Then, a specific identification input is sampled from the obtained stochastic process. Simulations results demonstrate the effectiveness of the proposed method.