This paper is concerned with chaoti cation of discrete dynamical systems in nite-dimensional real spaces, via feedback control techniques. A chaoti cation theorem for one-dimensional discrete dynamical systems and a chaoti cation theorem for general higher-dimensional discrete dynamical systems are established, respectively. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the maps corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions on two very small disjoint closed subsets in the domains of interest. This condition is weaker than those in the existing relevant literature.