ISS-equilibrium with stability analysis for disturbed game-based impulsive systems
This paper focuses on a class of two-player differential games subject to exogenous disturbances, where one player employs piecewise-continuous control, and the other uses impulsive control. Particularly, the exploration of equilibrium solution in differential games is accompanied by the stability p...
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| Published in | Automatica (Oxford) Vol. 179; p. 112394 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.09.2025
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0005-1098 |
| DOI | 10.1016/j.automatica.2025.112394 |
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| Abstract | This paper focuses on a class of two-player differential games subject to exogenous disturbances, where one player employs piecewise-continuous control, and the other uses impulsive control. Particularly, the exploration of equilibrium solution in differential games is accompanied by the stability performance analysis of relevant system. To be more specific, the construction of saddle point in zero-sum differential game and Nash equilibrium in nonzero-sum differential game is established under the Lyapunov criteria for input-to-state stability (ISS). Furthermore, owing to the existence of external disturbances and the characterization of ISS property, two extended equilibrium solution concepts are introduced. We propose the definition of ϵ-ISS saddle point and ϵ-ISS Nash equilibrium for which the corresponding verification theorems are formulated. Finally, two numerical experiments are provided to illustrate the proposed results. |
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| AbstractList | This paper focuses on a class of two-player differential games subject to exogenous disturbances, where one player employs piecewise-continuous control, and the other uses impulsive control. Particularly, the exploration of equilibrium solution in differential games is accompanied by the stability performance analysis of relevant system. To be more specific, the construction of saddle point in zero-sum differential game and Nash equilibrium in nonzero-sum differential game is established under the Lyapunov criteria for input-to-state stability (ISS). Furthermore, owing to the existence of external disturbances and the characterization of ISS property, two extended equilibrium solution concepts are introduced. We propose the definition of ϵ-ISS saddle point and ϵ-ISS Nash equilibrium for which the corresponding verification theorems are formulated. Finally, two numerical experiments are provided to illustrate the proposed results. |
| ArticleNumber | 112394 |
| Author | Liu, Wenlu Li, Chuandong Li, Xiaodi |
| Author_xml | – sequence: 1 givenname: Wenlu surname: Liu fullname: Liu, Wenlu email: uteaby@163.com organization: Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China – sequence: 2 givenname: Chuandong surname: Li fullname: Li, Chuandong email: cdli@swu.edu.cn organization: Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronic and Information Engineering, Southwest University, Chongqing 400715, PR China – sequence: 3 givenname: Xiaodi surname: Li fullname: Li, Xiaodi email: sodymath@163.com organization: School of Mathematics and Statistics, Shandong Normal University, Ji’nan, 250014, PR China |
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| Cites_doi | 10.1007/BF00929443 10.1109/9.273340 10.1016/j.automatica.2021.110077 10.1016/j.automatica.2022.110389 10.1137/S0363012900376013 10.1016/j.automatica.2008.03.021 10.1080/00207179.2016.1226518 10.1016/j.automatica.2022.110220 10.1016/j.nahs.2017.06.004 10.1287/moor.2021.1131 10.1287/opre.26.4.620 10.1007/s13235-021-00381-4 10.3934/jimo.2015.11.27 10.1007/s10479-018-2935-7 10.2307/1969529 10.1007/BF01189477 10.1007/s10957-013-0380-y 10.1109/TAC.2014.2362334 10.1016/j.automatica.2009.02.005 10.1016/j.ifacol.2016.10.310 10.1512/iumj.1984.33.33040 10.1287/moor.2019.0989 10.1239/jap/1276784895 10.1109/TSMC.2020.2964172 10.1109/STAB.2016.7541187 10.1109/TAC.2022.3206253 10.1137/120880094 10.1109/TAC.2015.2461851 10.1109/MSP.2012.2186410 |
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