Asymptotic inverse dynamics of feedback linearizable systems

Abstract

This paper considers the inverse dynamic problem for single-input single-output nonlinear systems. When the internal dynamics are 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 is shown that such an additional output can be defined so that the internal dynamics have solutions which are 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 referred to elastic robotic manipulators.