System identification: a learning theory approach

The problem of system identification is formulated as a problem in statistical learning theory, because statistical learning theory is devoted to the derivation of finite time estimates. If system identification is to be combined with robust control theory to develop a sound theory of indirect adaptive control, it is essential to have finite time estimates of the sort provided by statistical learning theory. As an illustration of the approach, a result is derived showing that in the case of systems with fading memory, it is possible to combine standard result's in statistical learning theory (suitably modified to the present situation) with some fading memory arguments to obtain finite time estimates of the desired kind. In the case of linear systems, the results proved here are not overly conservative, but are more so in the case of nonlinear systems where the adjustable parameters enter linearly into the model description. Though the actual results derived here are rather preliminary in nature, it is hoped that future researchers will pursue the ideas presented here to extend the theory further.