On input design for system identification in time domain

An input design problem for linear system identification is studied subject to an input amplitude constraint. First, the problem to find an optimal input sequence is formulated as a bilinear matrix inequality (BMI) optimization problem, where the optimality is defined based on the asymptotic variance property of the prediction error method in frequency domain. Since the solution of the BMI problem highly depends on the initial solution, the paper proposes to solve an optimal discrete spectrum design problem subject to an input power constraint, in order to give a valid initial solution for this problem. Then, the obtained optimal spectrum is approximately realized by a binary signal, which becomes a valid candidate of the initial solution. Finally, one local optimal solution is obtained through solving the locally linearized problem repetitively with the initial solution. In addition, the upper/lower bounds of the optimal value of the original problem is given via Parceval's relation. A numerical example demonstrates how the proposed method contributes to system identification.