The First Survey for Abilities of Wavelets in Solving Optimal Control Problems by Embedding Methods

Abstract

By a brief review on the applications of wavelets in
solving optimal control problems, a multiresolution analysis for
two dimensional Sobolev spaces and the square spline wavelets are
considered. Regarding the density and approximation properties
of these wavelets, for the ¯rst time, they are employed for solving
optimal control problems by embedding method. Existence and
the determination way for the solution are also discussed. Finally,
the abilities of the new approach are explained by a numerical
example and some comparisons.