Complexity of Identification of Input-Output Systems

The complexity of identification of abstract classes of input-output systems based on a finite number of input-output experiments is considered. It is proposed that an appropriate measure of the identification problem complexity is the size of the identification, defined as the minimum number of input-output experiments required to obtain an identification model. Lower bounds on the size for interpolative identifications are obtained in terms of the metric entropy of the class of systems. Estimates of the metric entropy of several classes of Lipschitz systems are obtained.