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Optimal Impulse Control and Impulse Game for Continuous-Time Deterministic Systems: A Review
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Keywords
Impulse Control
Impulsive Differential Systems
Continuous-Time Deterministic Systems
Optimal Control
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Abstract
Impulse control and impulsive games are fundamental in continuous-time deterministic systems, enabling the formulation and management of abrupt interventions within dynamic processes. This paper presents a comprehensive review of theoretical frameworks, methodologies, and practical applications of optimal impulse control and associated game-theoretic formulations. Key contributions include the synthesis of classical results from Pontryagin and Bellman with modern advancements in hybrid impulsive systems, delayed systems, and stochastic jump processes. Comparative analysis highlights the evolution of solution strategies, including dynamic programming, maximum principle formulations, and variational approaches. Findings indicate critical gaps in handling multi-delay systems, robustness under system perturbations, and implementation of finite versus infinite horizon impulsive games. The study consolidates insights from thirty seminal works, providing a foundation for future research and control system design.
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