Closed-loop model set validation under a stochastic framework

This paper deals with probabilistic model set validation. It is assumed that the dynamics of a multi-input multi-output (MIMO) plant is described by a model set with unstructured uncertainties, and identification experiments are performed in closed loop. A necessary and sufficient condition has been derived for the consistency of the model set with both the stabilizing controller and closed-loop frequency domain experimental data (FDED). In this condition, only the Euclidean norm of a complex vector is involved, and this complex vector depends linearly on both the disturbances and the measurement errors. Based on this condition, an analytic formula has been derived for the sample unfalsified probability (SUP) of the model set. Some of the asymptotic statistical properties of the SUP have also been briefly discussed. A numerical example is included to illustrate the efficiency of the suggested method in model set quality evaluation.