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Mathematics > Optimization and Control

arXiv:2108.13308 (math)
[Submitted on 30 Aug 2021 (v1), last revised 21 Aug 2023 (this version, v3)]

Title:GoPRONTO: a Feedback-based Framework for Nonlinear Optimal Control

Authors:Lorenzo Sforni, Sara Spedicato, Ivano Notarnicola, Giuseppe Notarstefano
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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.
Comments: 27 pages, 8 figures
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
Cite as: arXiv:2108.13308 [math.OC]
  (or arXiv:2108.13308v3 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.2108.13308

Submission history

From: Lorenzo Sforni [view email]
[v1] Mon, 30 Aug 2021 15:22:51 UTC (857 KB)
[v2] Tue, 31 Aug 2021 10:06:59 UTC (807 KB)
[v3] Mon, 21 Aug 2023 16:48:46 UTC (626 KB)
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