Frequency Domain Identification of Continuous-Time Systems : Reconstruction and Robustness
Abstract: Approaching parameter estimation from the discrete-time domain is the dominating paradigm in system identification. Identification of continuous-time models on the other hand is motivated by the fact that modelling of physical systems often take place in continuous-time. For many practical applications there is also a genuine interest in the parameters connected to these physical models.The most important element of time- and frequency-domain identification from sampled data is the discrete-time system, which is connected to the parameters of the underlying continuous-time system. For input-output models, it governs the frequency response from the sampled input to the sampled output. In case of time series, it models the spectrum of the sampled output.As the rate of sampling increase, the relationship between the discrete- and continuous-time parameters can become more or less ill-conditioned. Mainly, because the gathering of the poles of the discrete-time system around the value 1 in the complex plane will produce numerical difficulties while mapping back to the continuous-time parameters. We will therefore investigate robust alternatives to using the exact discrete-time system, which are based on more direct use of the continuous-time system. Another, maybe more important, reason for studying such approximations is that they will provide insight into how one can deal with non-uniformly sampled data.An equally important issue in system identification is the effect of model choice. The user might not know a lot about the system to begin with. Often, the model will only capture a particular aspect of the data which the user is interested in. Deviations can, for instance, be due to mis-readings while taking measurements or un-modelled dynamics in the case of dynamical systems. They can also be caused by misunderstandings about the continuous-time signal that underlies sampled data. From a user perspective, it is important to be able to control how and to what extent these un-modelled aspects influence the quality of the intended model.The classical way of reducing the effect of modelling errors in statistics, signal processing and identification in the time-domain is to introduce a robust norm into the criterion function of the method. The thesis contains results which quantify the effect of broad-band disturbances on the quality of frequency-domain parameter estimates. It also contains methods to reduce the effect of narrow-band disturbances or frequency domain outliers on frequency-domain parameter estimates by means of methods from robust statistics.
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