Singular output tracking by a polynomial approach

A constructive approach is proposed to solve the problem of singular output tracking for a class of nonlinear systems and output trajectories. The proposed polynomial controls are obtained by truncation of the formal power series associated with singular differential equations. The author gives the existence condition for these formal power series. The author shows that such a power series exists if an integer associated with the singular point x_s and a trajectory y_d, called rank of singularity and denoted by r(x_s,y_d) is infinite. The regularity of the control is studied using Newton´s polygons associated with singular differential equations