RESUMEN

The order reduction method for singularly perturbed optimal control systems consist of the setting the small parameter equal to zero and amploying the differenntial system thus obtained. Although in many situations this provides the corect variational limit problem, it is established in this paper that when considering system with non-scalar fast variables, the set of the systems for which the order reduction method is invalid is dense in the class of systems under consideration. This extends previous results, where only systems with linear fast variables were considered. The present result complements a result estabilished in a joint work with Artstein, where it was estabilished that the order reduction method is valid for singularly perturbed optimal control systems with scalar fast variable.