Dealing with Transients due to Multiple Experiments in Nonlinear System Identification*

Although in many static estimation problems the data are collected from repeated experiments, the default underlying (assumption) setting in most of the system identification tasks is that the data are generated from a single experiment. The rationale for this is that more data can be obtained by increasing the measurement time instead of doing more experiments. As the measurement time tends to infinity, under suitable assumptions it is possible to estimate consistently the model parameters. In most of the real life cases, however, increasing the measurement time is either not possible or it does not cover the whole operating range of the system to be identified, hence data from multiple experiments need to be combined. Furthermore, most of the real life systems are nonlinear and a large variety of nonlinear systems can be described by a nonlinear state space model structure. In this paper, a methodology to deal with the transients arising due to concatenating data from multiple experiments during the identification of Polynomial nonlinear state space (PNLSS) models is described. The methodology is validated on data generated from a laboratory experimental set-up.