Quasilinear controlled processes under conflict

In finite-dimensional Euclidean space, we analyze the problem of pursuit of a single evader by a group of pursuers, which is described by a system of differential equations with Caputo fractional derivatives of order \(alpha.\) The goal of the group of pursuers is the capture of the evader by at least \(m\) different pursuers (the instants of capture may or may not coincide). As a mathematical basis, we use matrix resolving functions that are generalizations of scalar resolving functions. We obtain sufficient conditions for multiple capture of a single evader in the class of quasi-strategies. We give examples illustrating the results obtained.

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“…In [6,7], Chikrii proposed a method of scalar resolving functions using Pontryagin's condition and, based on it, measurable choice theorems.…”

Section: Introductionmentioning

confidence: 99%

Matrix Resolving Functions in the Linear Group Pursuit Problem With Fractional Derivatives

Machtakova

Петров

2022

UMJ

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“…Depending on the degree to which the players are mutually informed as to the state of the process and the controls chosen by the opponent, the mathematical tools used may differ. The method of resolving functions and its diverse modifications [1,10] is conceptually close to Pontryagin's first direct method [3,6]. It has recently been subject to active development and is being used to solve some very complicated game problems, such as problems of group and successive pursuit and problems with phase constraints [1,7].…”

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confidence: 99%

“…We first consider the case ~(T,g(T), 7(T, ")) ~ M. Let x)r(') be an arbitrary measurable function with values in V. Proceeding as in the approach described in [1,10], we define a control function…”

mentioning

confidence: 99%