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A Comprehensive Analytical Framework for Impulse Control and Differential Game Strategies in Continuous-Time Deterministic Systems
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Keywords
Impulse control
differential games
continuous-time deterministic systems
optimal control
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Abstract
Impulse control and differential game strategies play a critical role in continuous-time deterministic systems, providing structured methods to manage abrupt state changes and optimize system performance. This paper develops a comprehensive analytical framework that integrates the principles of impulsive control with differential game theory, emphasizing their theoretical foundations, functional mechanisms, and practical applications. By synthesizing the extant literature on impulsive dynamic systems, optimal control methodologies, and time-delay analysis (Pontryagin, 1962; Bainov & Simeonov, 1989; Blaquiere, 1985), this study identifies core principles, compares methodological approaches, and highlights gaps in current research. The framework provides a unified perspective for the design, analysis, and implementation of impulse control strategies, offering insights into stability, performance optimization, and system robustness under deterministic dynamics. The findings demonstrate the efficacy of integrating differential game models with impulsive controls, enhancing system predictability and control precision while identifying future research directions in state-delay and hybrid control systems.
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