Identification of closed-loop linear systems using polyspectral analysis

In this dissertation, the problem of closed-loop system identification given noisy input-output measurements is considered. We discuss both the single-input single-output (SISO) and multi-input multi-output (MIMO) systems. We consider the “errors-in-variables” models, i.e., linear systems where measurements of both input and output of the system are noise contaminated. Attention is focused on frequency-domain approaches where the integrated polyspectrum (bispectrum or trispectrum) of the input and the integrated cross-polyspectrum, respectively, of the given time-domain input-output data are exploited. There exist several approaches to closed-loop system identification which require explicit noise modeling and/or knowledge of the controller. Moreover, in the presence of input measurement noise these approaches yield biased parameter estimates. In this dissertation we do not explicitly model noise.; It is assumed that the various disturbances/noise processes affecting the system are zero-mean stationary Gaussian, whereas the closed-loop system operates under an external non-Gaussian input which is not measured. Noisy measurements of the (direct) input and output of the plant are assumed to be available. The closed-loop system must be stable but it is allowed to be unstable in open-loop. 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 parametric system identification given consistent estimates of the underlying transfer function, are exploited. The parameter estimators are shown to be strongly consistent. For SISO system, we also investigate test the sensitivity of our proposed approaches to possible lack of system linearity. Asymptotic performance analysis and statistical model validation are also carried out for SISO systems.; The second set of approaches discussed in this dissertation are subspace-based identification techniques using polyspectral analysis. First the open-loop transfer function is estimated using the integrated polyspectrum and cross-polyspectrum of the time-domain input-output measurements. The obtained transfer function estimates are noise-corrupted. Then an existing subspace-based technique for parametric system identification given noisy measurements of the underlying transfer function, is adapted to apply to the problem under consideration. We show that the resultant transfer function estimator is strongly consistent.; Computer simulation examples are presented in support of the proposed approaches.