Uncertainty, Performance, and Model Dependency in Approximate Adaptive Nonlinear Control

We first consider systems satisfying a matching condition which are functionally known up to a L2 measure of uncertainty. A modified L2 measure of transient performance 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. The gain of the adaption mechanism is then fixed. Asymptotic analyses of the bounds under increasing model resolution are undertaken, and a sufficient condition on the Gram matrix of the bases of the models is given that ensures that the performance bounds are asymptotically independent of the 'size' of the model. Corresponding results can also be obtained for strict feedback systems, and this is briefly sketched, and some further developments are noted