Tracking through singularities using a robust differentiator

In this work, an alternative solution to the tracking problem for a SISO nonlinear dynamical system exhibiting points of singularity is given. An inversion-based controller is synthesized using the Flies generalized observability canonical form (GOCF) associated to the system. This form depends on the input and his derivatives. For this purpose, a robust exact differentiator is used for estimate control derivatives signals with the objective of define a control law depending on such derivatives estimates of the control and on the states of the system. This control law is such that when is applied to the system it guarantees bounded tracking error near the singularities.