Nonlinear map inversion via state observers

This paper deals with the problem of the inversion of nonlinear maps. The first contribution of the paper is the formal definition of some problems, already present in the literature, related to the inversion of nonlinear maps. The main contribution of the paper gives a unified solution to those problems, based on the use of observers for the state estimation of a nonlinear time-varying dynamical system associated with the given map. The proposed observer turns out to be an extension of well-known iterative methods for the solutions of nonlinear equations, such as the Newton and the gradient method.