  In this paper we We propose GoPRONTO, a first-order, feedback-based approach
to solve nonlinear discrete-time optimal control problems. This method is a
generalized first-order framework based on incorporating the original dynamics
into a closed-loop system. By exploiting this feedback-based shooting, we are
able to reinterpret the optimal control problem as the minimization of a cost
function, depending on a state-input curve, whose gradient can be computed by
resorting to a suitable costate equation. This convenient reformulation gives
room for a collection of accelerated numerical optimal control schemes. To
corroborate the theoretical results, numerical simulations on the optimal
control of a train of inverted pendulum-on-cart systems are shown.
