A pursuit-evasion differential game on a compact subset of ℝ^2 with geometric constraints

Authors

  • A. Asgharzadeh-Bonab AJA Command and Staff University, Tehran, Iran, Islamic Republic of
  • H. Bigdeli AJA Command and Staff University, Tehran, Iran, Islamic Republic of
  • J. Mohammadkarimi AJA Command and Staff University, Tehran, Iran, Islamic Republic of

DOI:

https://doi.org/10.31926/but.mif.2026.6.68.1.4

Keywords:

differential game, geometric constraint, non-convex

Abstract

In this paper, we study a pursuit differential game with many pursuers and evaders on a compact and not necessarily convex subset M of ℝ2. Their motion’s equation is a first-order differential equation. Players must play in this set M. For control functions of the players, we use geometric constraints. Completion of the pursuit means that the state of each of the evaders coincides with that of a pursuer in the plane. We derive sufficient conditions for completion of pursuit on this set M. We constructed a strategy of the pursuers that guarantees completion of the pursuit. Moreover, we construct winning strategies for pursuers.

Author Biographies

A. Asgharzadeh-Bonab, AJA Command and Staff University, Tehran, Iran, Islamic Republic of

Department of Science and Technology Studies

H. Bigdeli, AJA Command and Staff University, Tehran, Iran, Islamic Republic of

Department of Science and Technology Studies 

J. Mohammadkarimi, AJA Command and Staff University, Tehran, Iran, Islamic Republic of

Department of Science and Technology Studies

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Published

2026-06-23

Issue

Vol. 6(68) No. 1 (2026)

Section

MATHEMATICS