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

@misc{gbande2026analysis,
  title = {{Analysis of First-Order Linear Pursuit and Evasion Differential Games with Gronwall-Type Constraints}},
  author = {David Terna Gbande and Abbas Ja'afaru Badakaya and Jamilu Adamu and Mehdi Salimi},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30128},
  eprint = {2608.30128},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30128},
}

TY  - UNPB
TI  - Analysis of First-Order Linear Pursuit and Evasion Differential Games with Gronwall-Type Constraints
AU  - David Terna Gbande
AU  - Abbas Ja'afaru Badakaya
AU  - Jamilu Adamu
AU  - Mehdi Salimi
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30128
UR  - https://arxiv.org/abs/2608.30128
AB  - 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.
ER  -