Solving the global boundary problem for a nonlinear nonstationary controllable system

We propose algorithms for constructing differentiable controlling functions that are easily amenable for numerical implementation and guarantee a transition of a wide class of nonlinear and quasilinear systems of ordinary differential equations from the initial state to an arbitrary point in the phase space. We derive constructive sufficient conditions imposed on the right-hand side of the controllable system under which such a transition is possible. We consider the interorbital flight problem and perform numerical modeling for this problem.