Identification by the probability criterion
The paper deals with non-parametric identification of an abstract nonlinear system in a stochastic environment. Taking the mode of conditional probability density of system output given system input as the optimal model of system responses, a clustering-type identification algorithm is proposed for estimating system outputs from empirical input-output measurement data. The approach is based on a decomposition of input data into disjoint subsets and next finding for such a partition the corresponding output measurements possessing the largest number of close neighbours in the sample. This leads to a piecewise constant estimate of system outputs. Accuracy of the algorithm, in the sense of probability of \(\varepsilon\)-discrepancy between the system output and the output forecast computed according to the proposed routine, is studied and consistency of the resulting estimate is established, in particular. Also a lower bound for the membership probability of the output forecast to be in the most probable set of outputs is determined. A simple illustrative example is included.
scientific article; zbMATH DE number 1279859