$\Pi$-strategy for a differential game of pursuit with integral constraints of a generalized type

Abstract

The paper investigates a differential game of simple pursuit, when the controls of two opposing players are subject to integral constraints of a generalized type. The generalization of the proposed restriction lies in the fact that it includes previously known restrictions such as integral, geometric, linear, exponential and their mixtures. In general, it includes 25 types of pursuit problems with such different types of constraints. To solve the pursuit problem under such generalized constraints, we propose a parallel pursuit strategy ($\Pi$-strategy for short) and find sufficient conditions for the solvability of this problem. At the end of the article, tables are provided that list each particular type of game, the conditions for its solvability, the resolving function (which determines the corresponding $\Pi$-strategy), and the time of capture.

On the Lifeline Game of the Inertial Players with Integral and Geometric Constraints

“…For instance, the works of Mamadaliev [15][16][17] are devoted to linear pursuit games under integral constraints on players' controls with delay information. Thereafter, games with linear, linear-geometric, integro-geometric, and mixed constraints on controls were comprehensively solved using the Π-strategy in the works of Samatov et al [18,19].…”