Reachability of chaotic dynamic systems

This work focuses on the ability of any feedback approach to control a given chaotic system. The concept of reachability for nonlinear systems is presented in a differential geometric framework. This concept is used to examine the ability of any perturbation signal to redirect the system's trajectory flow within its phase space. The structure of the controlling input and its global relation to the underlying dynamics of the system are crucial for the ability to effectively control the system within the phase space. The concepts are illustrated on a well known example: the Lorenz system.