Aspects in Incomplete Modeling in System Identification

Sammanfattning: This thesis considers several aspects of the system identification problem. The major issues, however, are how one should represent and assess mode! errors. These issues have come to be central in system identification in recent years - mainly due to their relevance for robust control.The random error is the deviation between models based on finite data and infinite data. A measure of this error is the covariance matrix of the parameter estimate. An explicit expression for this covariance matrix has been known for long but, except under very restrictive assumptions, a consistent estimate has been missing. We derive two, conceptually different, simple, explicit and consistent estimation methods.A somewhat controversial issue in identification is whether disturbances should be considered as deterministic or stochastic. We show that, for prediction error methods or correlation methods, the input can be used to force a deterministic disturbance to behave like a stochastic disturbance from an identification point of view.Current mode! error problem formulations are somewhat ill-defined; it is in principle always possible to estimate the system perfectly asymptotically. We analyze a, perhaps more realistic, problem formulation which prevents this from being possible.When experimental data is sparse it is important to be able to incorporate prior knowledge of the system. A Bayesian procedure, suitable for transfer function estimation, is developed for this purpose.Mode! validation is another important issue. A standard procedure is to use statistical so called correlation tests. Previously it has been noticed that these tests may give levels of significance that differ from the desired ones. We show that it is possible to modify these tests so as to avoid this artifact.Spectral analysis is widely used for identification and time-series analysis. The method has previously been thoroughly analyzed from a quadratic mean point of view and here we complement this analysis with an almost sure convergence analysis.To support the analysis of the aforementioned methods a stochastic framework is developed. Byproducts of this are extensions of some convergence results for prediction error methods and instrumental variable methods.