Open-loop vs. closed-loop identification of Box-Jenkins systems in a least costly identification context

In this paper, we compare open-loop and closed-loop prediction error identification. In particular, we determine whether open-loop or closed-loop identification is optimal in the least costly identification experiment design framework. The least costly experiment design framework is a new framework for optimal experiment design where the objective is to determine the cheapest identification while ensuring that the accuracy of the identified model is above some nominated threshold. A second contribution of this paper is to develop a control design algorithm which ensures that the designed controller both ensures sufficient closed-loop performance with the true system, but also ensures that a model identified via closed-loop identification on the designed loop has high accuracy.