Identification of model uncertainty for control design

This thesis deals with the problem of model uncertainty quanti cation from exper imental data Given a set of measured input and output data points the aim is to establish an upper bound on a relevant norm on the di erence between the true system and a suitable model of that system More speci cally the problem addressed in this thesis is how one should represent and quantify model errors in such a way that the identi cation result is suitable to serve as a basis for high performance robust control design A critical evaluation of the related literature is made showing that a major part of the problem is shifted to the prior information while no adequate procedures exist to obtain this information A rst approach towards solving the problem makes use of a hard upper bound on the noise in the frequency domain as prior information and yields a hard worst case error bound First an error bound on a nite number of frequency points is established and subsequently this error bound is interpolated The merit of this procedure is that the model with respect to which the error bound is calculated can be speci ed by the user A major disadvantage is however that the necessary prior information is hard to obtain Based on an extensive evaluation of options and consequences a mixed averaging worst case embedding of the modelling errors now is proposed to e ectively account for accumulations of both random as well as structural errors in a situation where only the dominant part of the system is linear and time invariant That is we argue that the noise should be considered as stochastic whereas undermodelling should be regarded as unknown but bounded Given this choice for the embedding a second procedure is presented to estimate a model together with a bound on the model uncertainty from experimental data A periodic input signal and data segmentation are employed to e ectively distinguish between the random and structural errors A model is estimated over each period of the input signal which results in a set of models The average over this set of models yields the nal estimate while the mutual di erences between the models in the set provide information about the uncertainty in this nal estimate Specializing to linear time invariant systems with stochastic noise a closed form con dence interval for the error due to the noise now can be obtained asymptotically in the number of