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 l inearizable, it can be extremely difficult, if not impossible, to cons truct an exact feedback linearizing transformation. For nonfeedback li nearizable systems, one can find (at least formally) an approximating feedback linearizable system for which a transformation can be constru cted. We provide a new algorithm 1) to construct an approximating tran sformation for a feedback linearizable system, and 2) to construct an approximating transformation for a system that is not feedback lineari zable. Instead of approximating the given nonlinear system, we approxi mate the transformation in a ''proper'' sense. We assume the lead vari ables 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'') transfor mations in a surprisingly small number of steps.