QUANTIFICATION OF UNCERTAINTY IN TRANSFER-FUNCTION ESTIMATION - A MIXED PROBABILISTIC - WORST-CASE APPROACH

In this paper an identification problem is solved which is directed to wards the use of the identified model as a basis for robust control de sign. A procedure is presented to identify, on the basis of time domai n measurement data, a reduced order finite impulse response (FIR) mode l together with an upper bound on the model error of the corresponding transfer function, using only minor prior information. We assume the measurement data to contaminated with a stochastic noise disturbance u nknown spectral properties. By applying a procedure similar to Bartlet t's procedure of periodogram averaging, in conjunction with a periodic input signal, the statistics of the model error asymptotically can be obtained from the data. The model error consists of two parts: a prob abilistic part, due to the stochastic noise disturbance, and a worst-c ase part, due to the unmodelled dynamics. The latter is explicitly bou nded with a hard error bound, while for the former a confidence interv al can be specified asymptotically. This enables an explicit trade-off between undermodelling (bias) and variance terms. The resulting error bound appears to be tight.