DIFFERENTIAL L-CAPTURE AND EVASION GAMES WITH INERTIAL PLAYERS UNDER GEOMETRIC CONSTRAINTS ON CONTROLS: DIFFERENTIAL L-CAPTURE AND EVASION GAMES WITH INERTIAL PLAYERS UNDER GEOMETRIC CONSTRAINTS ON CONTROLS

Bahrom Samatov; Mohisanam Turgunboeva

doi:10.52754/16948645_2023_2_202

Authors

Tadjiahmatovich Namangan State University
Akhmadullo kizi Namangan State University

DOI:

https://doi.org/10.52754/16948645_2023_2_202

Keywords:

Differential game, l-capture, evasion, pursuer, evader, geometric constraint, strategy, guaranteed time of l-capture

Abstract

This paper is devoted to solve l-capture and evasion problems for a differential game of two players, a pursuer and an evader, with inertial motions. We impose geometric constraints on controls of the players. Originally, we devise an l-approach strategy, on the basis of Chikrii’s method of resolving functions, for a pursuer and we present new sufficient conditions of l-capture. Here as l-capture, we refer the moment when a pursuer approaches an evader at the range l>0. In the evasion problem we define the strategy guaranteeing an evader to diverge from a pursuer at the distance greater than l>0. Besides that, new sufficient conditions of evasion have been shown.

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DIFFERENTIAL L-CAPTURE AND EVASION GAMES WITH INERTIAL PLAYERS UNDER GEOMETRIC CONSTRAINTS ON CONTROLS