arXiv subjects

Jamilu Adamu

Publications and source records attributed to Jamilu Adamu.

4 recordsLinked to original sources

arXiv2026

New strategies for some pursuit-evasion differential games with Gronwall-type constraints

This paper studies a class of non-cooperative pursuit-evasion differential games in the sequence space $l_{2}.$ The motions of the pursuer and the evader are described by certain first-order differential equations while their control functions are subject to Gronwall-type constraints which impose history-dependent bounds on their control resources. Two fundamental problems are investigated. For the pursuit problem, new strategy for the pursuer is constructed and sufficient conditions guaranteeing the completion of pursuit are established. For evasion problem, an admissible strategy of the evader ensuring avoidance of capture is obtained, and corresponding sufficient conditions for successful evasion are derived. The proposed approached extends existing results on differential games with classical geometric and integral constraints to a broader class of systems governed by Gronwall-type restrictions.

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arXiv2026

Interception Conditions in Multi-Agent Pursuit Games Governed by Linear Dynamics with Gronwall-type Constraints

This paper investigates a multi-agent pursuit problem in which a group of pursuers seeks to intercept one or more evaders within a fixed operational time horizon. The motion of both pursuers and evaders is described by first-order linear differential equations, and the control inputs available to the agents are subject to Gronwall-type constraints. Pursuit is considered successful when at least one pursuer reaches the position of each evader at a finite time within the prescribed duration. Within this framework, we construct permissible strategies for the pursuers and derive sufficient conditions under which interception is guaranteed despite the evaders' counteractions. To support the theoretical results, we present numerical examples that demonstrate the effectiveness of the proposed strategies and confirm the analytical conditions for successful pursuit.

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arXiv2026

Analysis of First-Order Linear Pursuit and Evasion Differential Games with Gronwall-Type Constraints

We examine pursuit and evasion problems in the space $ \mathbb{R}^{n} $ involving a lone pursuer and evader. Motion of each player is governed by a first-order linear differential equation. The players' control functions are subject to the Gronwall-type inequality. The game's duration is fixed and represented by a positive number $\vartheta $. When the state of a pursuer coincides with that of the evader, we then say the pursuit is completed. On the contrary, evasion is possible when throughout the game there is no agreement between the states of pursuer and evader. The result obtained related to the pursuit problem depends on the attainability domains of the two players. On the other hand, one sufficient condition is given for evasion to be possible.

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arXiv2026

Solution and Optimal Strategies for a Differential Game of Pursuit-Evasion with Point-Wise Constraints

This work study a differential game of pursuit-evasion involving countably many pursuers $p_{1},p_{2},\cdots,p_{m}$ and a single evader $e$ under point-wise (geometric) constraints in the sequence space $l_{2}.$ The pursuers evolve according to specified differential equations of $1^{st}$ order while the evader follows a $2^{nd}$ order differential equation. The game period is a fixed time interval of length $\theta$ unit of time. The minimum distance between evader and the pursuer at the terminal time denotes the game payoff. The pursuers aim is to minimize the payoff, whereas the evader seeks to maximize it. We obtain the solution of the game, including optimal strategies of the players construction, as well as game value estimation.

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