Origin-Transfer Geometric Constraint Pursuit Game Modelled by Infinite System of Dyadic Differential Equations

Abstract

This paper investigates a zero-sum two-person pursuit differential game modelled by an infinite system of dyadic differential equations. The two players in the game are a pursuing player and an evading player; their control functions adhere to geometric constraints, and the control resources available to the pursuing player is more than those of the evading player. The pursuing player is intent on driving the system’s state from the initial state ξ₀ to ℓ₂ space origin in a finite period of time while the evading player is counteracting this. For the control problem, we design an admissible control that can steer the system’s state to the origin and for the differential game problem, we develop an admissible strategy for the pursuing player that helps realize the objective and the guaranteed pursuit time equation. An illustrative example to show how our results can be applied to determine pursuit completion and compute guaranteed pursuit time in our differential game model is provided.