A NEW ALGORITHM FOR CONSTRUCTING APPROXIMATE TRANSFORMATIONS FOR NONLINEAR-SYSTEMS

Feedback linearization has proved to be a tremendously useful tool in nonlinear systems and control. However, even if a system is feedback linearizable, it can be extremely difficult, if not impossible, to construct an exact feedback linearizing transformation. For nonfeedback linearizable systems, one can find (at least formally) an approximating feedback linearizable system for which a transformation can be constructed. We provide a new algorithm 1) to construct an approximating transformation for a feedback linearizable system, and 2) to construct an approximating transformation for a system that is not feedback linearizable. Instead of approximating the given nonlinear system, we approximate the transformation in a ''proper'' sense. We assume 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.