Arie Leizarowitz, Technion"On the order reduction method for singularly perturbed optimal control problems" AbstractThe order reduction method for singularly perturbed optimal control systems consists of employing he system which is obtained while setting the small parameter equal to zero. In many cases the differential algebraic system thus obtained indeed provides an appropriate approximation to the singularly perturbed problem under consideration. There are, however, many other cases where it does not. In this talk I will present a simple condition which distinguishes between these two situations. Concerning this issue, the dimension of the fast variable is a crucial quantity: If it is 1, then order reduction is valid. If, however, it is larger than 1, then the set of optimal control systems for which order reduction is not valid is dense (in the $L_{\infty }$ norm) in the class of systems which we consider. TUESDAY, November 26, 2002 |