Optimal Input Signal Design for a Second Order Dynamic System Identification Subject to D-Efficiency Constraints

摘要

System identification, in practice, is carried out by perturbing processes or plants under operation. That is why in many industrial applications an optimal input signal would be preferred for system identification. In this case, the objective function was formulated through maximisation of the Fisher information matrix determinant (D-optimality) expressed in conventional Bolza form. As setting such conditions of the identification experiment we can only say about the D-suboptimality, we quantify the plant trajectories using the D-efficiency measure. An additional constraint, imposed on D-efficiency of the solution, should allow to attain the most adequate contents of information from the plant which operating point is perturbed in the least invasive way. A simple numerical example, which clearly demonstrates the idea presented in the paper, is included and discussed.