  In this paper, we consider the problems of approximating uncertainties and
feedback control for a class of nonlinear systems without full-known states,
and two approximation methods are proposed: universal approximation using
integral-chain differentiator or extended observer. Comparing to the
approximations by fuzzy system and radial-based-function (RBF) neural networks,
the presented two methods can not only approximate universally the
uncertainties, but also estimate the unknown states. Moreover, the
integral-chain differentiator can restrain noises thoroughly. The theoretical
results are confirmed by computer simulations for feedback control.
