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

We consider systems satisfying a matching condition that are functionally known up to weighted L² and L^∞ measures of uncertainty. A modified LQ measure of control and state transient performance is given, and the performance of a class of approximate-model-based adaptive controllers is studied. An upper performance bound is derived in terms of the uncertainty models (the stability and state transient bounds require only the La uncertainty model; control effort bounds require both L² and L^∞ uncertainty models) and various structural properties of the model basis. Sufficient conditions are given to ensure that the performance is bounded independently of the model basis size