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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Bibliographic Details
Published inAutomatica (Oxford) Vol. 179; p. 112394
Main Authors Liu, Wenlu, Li, Chuandong, Li, Xiaodi
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.09.2025
Subjects
Differential game
Impulsive control
Input-to-state stability
Nash equilibrium
Saddle point
Nash equilibrium
Impulsive control
Differential game
Input-to-state stability
Saddle point
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ISSN0005-1098
DOI10.1016/j.automatica.2025.112394

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Summary: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.
ISSN:0005-1098
DOI:10.1016/j.automatica.2025.112394