  In this paper, we study the use of state-of-the-art nonlinear system
identification techniques for the optimal control of nonlinear systems. We show
that the nonlinear systems identification problem is equivalent to estimating
the generalized moments of an underlying sampling distribution and is bound to
suffer from ill-conditioning and variance when approximating a system to high
order, requiring samples combinatorial-exponential in the order of the
approximation, i.e., the global nature of the approximation. We show that the
iterative identification of "local" linear time varying (LTV) models around the
current estimate of the optimal trajectory, coupled with a suitable optimal
control algorithm such as iterative LQR (ILQR), is necessary as well as
sufficient, to accurately solve the underlying optimal control problem.
