Linear Differential Game Problem with Generalized Integral Constraints

U. M. Nasir1, B. I. Bukar Bukar1 & B. A. Madu2

1Département of Mathematics and Statistics, Yobe State University
2Department of Mathematics, University of Maiduguri

*Corresponding author’s Email: bgkrs030@gmail.com, doi.org/10.55639/607.02010028


ABSTRACT

This paper examines a pursuit differential game problem involving one pursuer and one evader in n-dimensional spaces (Rn), where a pursuer aims to intercept an evader with minimal time. We consider a game-theoretic framework with generalized integral constraints on the pursuer’s control inputs where we derive optimal pursuit strategies for the pursuer and evader in n-dimensional spaces using the Pontryagin Maximum Principle. The findings show that the pursuer’s optimal strategy involves moving towards the evader at maximum speed. In contrast, the evader’s optimal strategy involves maintaining a constant velocity, and we provide numerical examples to illustrate the effectiveness of our approach. The study establishes sufficient conditions for ensuring the successful completion of the pursuit also, as well as exploring the feasibility of integrating the players’ dynamic equations with the given constraints to address the challenges in solving pursuit and evasion differential games.

Keywords:

Differential Equation,
Pursuit-evasion
games,
Optimal control,
Dynamic games