Quantification of model uncertainty from experimental data: a mixed deterministic-probabilistic approach

In this paper a procedure is presented to obtain an upper bound on the modelling error for a reduced order finite impulse response (FIR) estimate of the transfer function of a linear system, using only minor a priori information. By applying a procedure similar to Bartlett´s procedure of periodogram averaging to the FIR estimate, in conjunction with a periodic input signal, the statistics of the modelling error asymptotically can be obtained from the data. The modelling error consists of two parts: an averaging (probabilistic) part, due to the stochastic noise disturbance on the data, and a worst case (deterministic) part, due to the unmodelled dynamics. The latter is explicitly bounded with a hard error bound, while for the former a confidence interval can be specified asymptotically. The resulting error bounds appear to be highly realistic and, as a consequence, suitable for high performance robust control design purposes