On Controllability of Some Classes of Affine Nonlinear Systems

Abstract: In this paper, we will present some recent progress in both global controllability and global asymptotical controllability of affine nonlinear systems. Our method is based on some basic facts in planar topology and in the geometric theory of ordinary differential equations. We will first present a necessary and sufficient condition for global controllability of general planar affine nonlinear systems, and then will give its generalizations to some high dimensional systems. Asymptotical controllability results will also be discussed and necessary and sufficient conditions will also be presented. Finally, we will show that the new controllability criterion can be easily applied to a number of practical examples.