  We examine the problem of two-point boundary optimal control of nonlinear
systems over finite-horizon time periods with unknown model dynamics by
employing reinforcement learning. We use techniques from singular perturbation
theory to decompose the control problem over the finite horizon into two
sub-problems, each solved over an infinite horizon. In the process, we avoid
the need to solve the time-varying Hamilton-Jacobi-Bellman equation. Using a
policy iteration method, which is made feasible as a result of this
decomposition, it is now possible to learn the controller gains of both
sub-problems. The overall control is then formed by piecing together the
solutions to the two sub-problems. We show that the performance of the proposed
closed-loop system approaches that of the model-based optimal performance as
the time horizon gets long. Finally, we provide three simulation scenarios to
support the paper's claims.
