Adaptive nonlinear control with nonlinear swapping

We present a new approach to adaptive nonlinear control based on a complete controller-identifier separation which has long been a goal in adaptive system design. In this approach it is possible not only to separately design and analyze the parameter identifier, but also to independently guarantee properties achieved by the controller. Our controllers guarantee input-to-state stability with respect to the parameter error and its derivative as inputs. The parameter identifiers, in turn, guarantee boundedness of these signals. A key ingredient in the identifier design, as well as the convergence analysis, is a nonlinear generalization of the famous swapping lemma. The identifiers are based both on the plant model and the error system and allow a wide variety of update laws-gradient and least-squares, normalized and unnormalized.