Rm. Hirschorn et E. Arandabricaire, GLOBAL APPROXIMATE OUTPUT TRACKING FOR NONLINEAR-SYSTEMS, IEEE transactions on automatic control, 43(10), 1998, pp. 1389-1398
This paper addresses the global output tracking problem for nonlinear
systems with singular points. For nonlinear systems which satisfy a su
itable observability condition, the authors identify a class of smooth
output trajectories which the system can track using continuous open-
loop controls. This class includes all output trajectories generated b
y smooth state feedback. They then study the problem of approximate ou
tput tracking using discontinuous time-varying feedback controllers. G
iven a smooth output trajectory for which exact tracking is possible,
the authors construct a discontinuous feedback controller which achiev
es robust tracking of the desired output trajectory in the face of per
turbations. Finally, it is shown that their results can be applied to
the control of a chain system, and some numerical results are presente
d to illustrate the performance of their controller.