Point-to-point control for nonlinear systems

This work deals with point-to-point control of nonlinear systems. That is, given two vectors xi gE Rn, i = 1, 2, and a number tf > 0. The point-to-point control problem is to find a control function v(t) ε Rm, t ε [0, tf], n ≥ m, acting as an input to a nonlinear system such that the systemʹs state x(t) ε Rn, t ε [0, tf], will satisfy the condition: if x(0) = x1 then x(tf) = x2. The existence of such a control function depends on some measure of controllability of the system