GoPRONTO: a Feedback-based Framework for Nonlinear Optimal Control

Abstract: 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.