Cargando…
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...
Autores principales: | , |
---|---|
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 |
_version_ | 1784786568779661312 |
---|---|
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. |
format | Online Article Text |
id | pubmed-9459680 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT xiaxing anonlinearfinitetimerobustdifferentialgameguidancelaw AT caiyuanli anonlinearfinitetimerobustdifferentialgameguidancelaw AT xiaxing nonlinearfinitetimerobustdifferentialgameguidancelaw AT caiyuanli nonlinearfinitetimerobustdifferentialgameguidancelaw |