Asymptotic inverse dynamics of non-linear systems

Abstract

The inverse dynamic problem for single-input single-output non-linear systems is considered. When the internal dynamics arc not stable, an asymptotic inverse dynamic problem is introduced that can be solved by introducing an additional output map. In particular, with reference to systems linearizable via feedback, it has been shown that such an additional output can be defined so that the internal dynamics have solutions uniform-asymptotically stable for any given reference output. The singular perturbation theory is used to simplify the computation of the reference trajectory for the additional output from the given reference output. The paper is completed by an example referring to elastic robotic manipulators.