LINEAR PURSUIT–EVASION DIFFERENTIAL GAMES WITH JOINT CONTROL CONSTRAINTS
Keywords:
Keywords: Differential games; pursuit–evasion; joint control constraints; saddle–point equilibrium; linear systems; resource sharing.Abstract
Annotation:This paper studies linear pursuit–evasion differential games under joint control constraints that reflect shared limitations on players’ actions. Unlike classical models with independent controls, the admissible strategies are coupled through a common feasibility set. The analysis focuses on the impact of such constraints on equilibrium existence, strategy structure, and system trajectories. The results show that joint constraints significantly modify optimal behavior and introduce implicit coordination between antagonistic agents. The proposed framework is relevant for applications in robotics, security systems, and regulated economic environments where shared resources are present.
References
1. Isaacs, R. (1965). Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. New York: John Wiley & Sons.
2. Bardi, M., & Capuzzo-Dolcetta, I. (1997). Optimal Control and Viscosity Solutions of Hamilton–Jacobi–Bellman Equations. Boston: Birkhäuser.
3. Karimov, E. T., & Usmanov, M. A. (2015). Differensial o‘yinlar nazariyasi va uning tatbiqlari [Theory of Differential Games and Its Applications]. Tashkent: Fan Publishing House.
4. Rakhimov, S. R. (2018). Linear pursuit–evasion games with constrained controls. Uzbek Journal of Mathematical Sciences, 2(1), 45–56.
5. Akhmedov, B. A., & Khasanov, A. U. (2020). Optimal control problems with joint constraints in dynamic systems. Bulletin of Tashkent State Technical University, 3, 28–35.
