Global Approximate Output Tracking for Nonlinear Systems

This paper addresses the global output tracking problem for nonlinear systems with singular points. For nonlinear systems which satisfy a suitable observability condition, we identify a class of smooth output trajectories which the system can track using continuous open loop controls. This class includes all output trajectories generated by smooth state state feedback. We then study the problem of approximate output tracking using discontinuous time-varying feedback controllers. Given a smooth output trajectory for which exact tracking is possible, we construct a discontinuous feedback controller which achieves robust tracking of the desired output trajectory in the face of perturbations. Finally, it is shown that our results can be applied to the control of a chain system, and some numerical results are presented to illustrate the performance of our controller.