A new algorithm for constructing approximate transformations for nonlinear systems

An algorithm is provided for constructing an approximating transformation for a feedback linearizable system, and for a system that is not feedback linearizable. Instead of approximating the given nonlinear system, the authors approximate the transformation in a proper sense. They assume that the lead variables of a transformation have a certain form with unknown parameters, substitute these variables into the required equations, and determine the unknown parameters through linear algebraic equations. There is a tremendous savings in terms of number of equations and unknowns, and it is sometimes possible to find exact (or best possible) transformations in a surprisingly small number of steps