Use of observers for the inversion of nonlinear maps

In this paper we deal with the problem of the inversion of nonlinear maps. The first contribution of the paper is the definition, in a formal framework, of some problems related to map inversion, which are already present in the literature, for instance in the robotics area and in observer theory. The second and the main contribution consists in the solution of such problems by means of observers, for which some structures are proposed, for the state estimation of a time-varying nonlinear system associated with the given map and reference trajectory.