Output Tracking Through Singularities

Abstract

In this paper we consider the tracting problem for single-input, single-output nonlinear systems, affine in the control and where f, g and h are analytic. In the tracking problem one is given a function y and considers conditions under which there exists a control ud, and corresponding state trajectory xd, so that the output of the initialized system coincides with yd on some time interval [0, T]. If T is alowed to be arbitrarily small then the solution is well studied. We are concerned here with one problem which occurs when trying to extend these results to the case where T is specified a priori. There are many applications of singular tracking, namely in robotics. This study pursues the analysis begun by Hirschorn and Davis. It is introduced further structure which is important in quantifying smoothness of solutions to the problem. Specific results are given in the particular case of time-varying linear systems.KeywordsSingular PointSingular SystemTracking ProblemAdmissible PairOpen Loop ControlThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.