On the Non-Validity of the Order Reduction Method for Singularly Perturbed Control Systems.

The order reduction method for singularly perturbed optimal control systems consists of setting the small parameter equal to zero and employing the differential system thus obtained. Although in many situations this provides the correct variational limit problem, it is established in this paper that when considering systems with non-scalar fast variables, the set of 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 established in a joint work with Artstein, where it was established that the order reduction method is valid for singularly perturbed optimal control systems with scalar fast variable. [ABSTRACT FROM AUTHOR]