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A Nonlinear Finite-Time Robust Differential Game Guidance Law

In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs equation, a t...

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Autores principales: Xi, Axing, Cai, Yuanli
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9459680/
https://www.ncbi.nlm.nih.gov/pubmed/36081109
http://dx.doi.org/10.3390/s22176650
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author Xi, Axing
Cai, Yuanli
author_facet Xi, Axing
Cai, Yuanli
author_sort Xi, Axing
collection PubMed
description In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs equation, a time-varying cost function is developed to reflect the fixed terminal time, and the robust guidance law is developed to compensate for the external disturbance. Then, a novel neural network identifier is designed to approximate the unknown nonlinear dynamics with online weight tuning. Subsequently, an online critic neural network approximator is presented to estimate the cost function, and time-varying activation functions are considered to deal with the fixed final time problem. An adaptive weight tuning law is given, where two additional terms are added to ensure the stability of the closed-loop nonlinear system and so as to meet the terminal cost at a fixed final time. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic neural network weights estimation error are proven based upon the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed robust differential game guidance law for nonlinear interception.
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spelling pubmed-94596802022-09-10 A Nonlinear Finite-Time Robust Differential Game Guidance Law Xi, Axing Cai, Yuanli Sensors (Basel) Article In this paper, a robust differential game guidance law is proposed for the nonlinear zero-sum system with unknown dynamics and external disturbances. First, the continuous-time nonlinear zero-sum differential game problem is transformed into solving the nonlinear Hamilton–Jacobi–Isaacs equation, a time-varying cost function is developed to reflect the fixed terminal time, and the robust guidance law is developed to compensate for the external disturbance. Then, a novel neural network identifier is designed to approximate the unknown nonlinear dynamics with online weight tuning. Subsequently, an online critic neural network approximator is presented to estimate the cost function, and time-varying activation functions are considered to deal with the fixed final time problem. An adaptive weight tuning law is given, where two additional terms are added to ensure the stability of the closed-loop nonlinear system and so as to meet the terminal cost at a fixed final time. Furthermore, the uniform ultimate boundedness of the closed-loop system and the critic neural network weights estimation error are proven based upon the Lyapunov approach. Finally, some simulation results are presented to demonstrate the effectiveness of the proposed robust differential game guidance law for nonlinear interception. MDPI 2022-09-02 /pmc/articles/PMC9459680/ /pubmed/36081109 http://dx.doi.org/10.3390/s22176650 Text en © 2022 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Xi, Axing
Cai, Yuanli
A Nonlinear Finite-Time Robust Differential Game Guidance Law
title A Nonlinear Finite-Time Robust Differential Game Guidance Law
title_full A Nonlinear Finite-Time Robust Differential Game Guidance Law
title_fullStr A Nonlinear Finite-Time Robust Differential Game Guidance Law
title_full_unstemmed A Nonlinear Finite-Time Robust Differential Game Guidance Law
title_short A Nonlinear Finite-Time Robust Differential Game Guidance Law
title_sort nonlinear finite-time robust differential game guidance law
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9459680/
https://www.ncbi.nlm.nih.gov/pubmed/36081109
http://dx.doi.org/10.3390/s22176650
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