Uncertainty, performance, and model dependency in approximate adaptive nonlinear control

We consider systems satisfying a matching condition which are functionally known up to a L² measure of uncertainty. A modified L² performance measure is given, and the performance of a class of model based adaptive controllers is studied. An upper performance bound is derived in terms of the uncertainty measure and measures of the approximation error of the model. Asymptotic analyses of the bounds under increasing model size are undertaken, and sufficient conditions are given on the model that ensure the performance bounds are bounded independent of the model size