On the construction of solutions of terminal problems for multidimensional affine systems in quasicanonical form

We consider the construction of solutions of terminal problems for multidimensional affine systems. We show that the terminal problem for a regular system in quasicanonical form can be reduced to a boundary value problem for a system of ordinary differential equations of lower order with right-hand side depending on a vector parameter. We prove a sufficient condition for the existence of a solution of the above-mentioned boundary value problem. A method for constructing a numerical solution is developed.