On closed-loop system identification using polyspectral analysis given noisy input-output time-domain data

The problem of closed-loop system identification given noisy input-output m easurements is considered. It is assumed that the closed-loop system operat es under an external non-Gaussian input which is not measured. If the exter nal input has non-vanishing integrated bispectrum (IB) and data IB is used for identification, then the various disturbances/noise processes affecting the system are assumed to be zero-mean stationary with vanishing IB. If th e external input has non-vanishing integrated trispectrum (IT) and data IT is used for identification, then the various disturbances/noise processes a ffecting the system are assumed to be zero-mean stationary Gaussian. Noisy measurements of the (direct) input and output of the plant are assumed to b e available. The closed-loop system must be stable but it is allowed to be unstable in open loop. Parametric modeling of the various noise sequences a ffecting the system is not needed. First the open-loop transfer function is estimated using the integrated polyspectrum and cross-polyspectrum of the time-domain input-output measurements. Then two existing techniques for par ametric system identification given consistent estimates of the underlying transfer function, are exploited. The parameter estimators are strongly con sistent. Asymptotic performance analysis is also carried out. A computer si mulation example using an unstable open-loop system is presented to illustr ate the proposed approach. (C) 2000 Elsevier Science Ltd. All rights reserv ed.