GoPRONTO: a Feedback-based Framework for Nonlinear Optimal Control

TL;DR

GoPRONTO introduces a feedback-based first-order framework for solving nonlinear discrete-time optimal control problems, leveraging a closed-loop system approach and costate equations to enable accelerated numerical schemes.

Contribution

It presents a novel feedback-based shooting method that reformulates nonlinear optimal control as a cost minimization problem with efficient gradient computation.

Findings

Numerical simulations demonstrate the effectiveness of GoPRONTO on inverted pendulum systems.

The framework allows for accelerated convergence in solving nonlinear optimal control problems.

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.