Optimal Control of Discrete-Time Nonlinear Systems

Fuente: arXiv
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Main Authors: Lv, Chuanzhi, Yin, Xunmin, Li, Hongdan, Zhang, Huanshui
Format: Preprint
Published: 2024
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author Lv, Chuanzhi
Yin, Xunmin
Li, Hongdan
Zhang, Huanshui
author_facet Lv, Chuanzhi
Yin, Xunmin
Li, Hongdan
Zhang, Huanshui
contents This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time constraints. While linearization methods are computationally efficient, their inherent low accuracy can compromise control precision and overall performance. To address this challenge, this study proposes a novel approach based on the optimal control method. Firstly, the original optimal control problem is transformed into an equivalent optimization problem, which is resolved using the Pontryagin's maximum principle, and a superlinear convergence algorithm is presented. Furthermore, to improve computation efficiency, explicit formulas for computing both the gradient and hessian matrix of the cost function are proposed. Finally, the effectiveness of the proposed algorithm is validated through simulations and experiments on a linear quadratic regulator problem and an automatic guided vehicle trajectory tracking problem, demonstrating its ability for real-time online precise control.
format Preprint
id arxiv_https___arxiv_org_abs_2411_01484
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Optimal Control of Discrete-Time Nonlinear Systems
Lv, Chuanzhi
Yin, Xunmin
Li, Hongdan
Zhang, Huanshui
Optimization and Control
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time constraints. While linearization methods are computationally efficient, their inherent low accuracy can compromise control precision and overall performance. To address this challenge, this study proposes a novel approach based on the optimal control method. Firstly, the original optimal control problem is transformed into an equivalent optimization problem, which is resolved using the Pontryagin's maximum principle, and a superlinear convergence algorithm is presented. Furthermore, to improve computation efficiency, explicit formulas for computing both the gradient and hessian matrix of the cost function are proposed. Finally, the effectiveness of the proposed algorithm is validated through simulations and experiments on a linear quadratic regulator problem and an automatic guided vehicle trajectory tracking problem, demonstrating its ability for real-time online precise control.
title Optimal Control of Discrete-Time Nonlinear Systems
topic Optimization and Control
url https://arxiv.org/abs/2411.01484