Input design for Bayesian frequency response identification via convex programming

Abstract

This paper proposes a novel approach for the input design of the Bayesian frequency response identification. The input design problem is first formulated by considering deterministic inputs, which leads to a non-convex optimization problem. Restricting inputs to be periodic makes the problem convex but introduces conservativeness. 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. A multiplied sampled input turns out to be the good input with a certain probability. Then, the optimal input is selected to be the minimum energy one among the good inputs. Simulations results demonstrate the effectiveness of the proposed method.