<p>A pursuit differential game problem with players’ motions and controls in the sequence space <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2785_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">$l_\infty $</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>l</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> is considered in this paper. Controls of finite number of pursuers and one evader are subject to component-wise integral constraints. It has been established that there exist admissible strategies of pursuers such that <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2785_Article_IEq4.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="88" /> </InlineMediaObject> <EquationSource Format="TEX">$x_{{\hat{i}}}(\theta ) = y(\theta )$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>x</mi> <mover accent="true"> <mi>i</mi> <mo stretchy="false">^</mo> </mover> </msub> <mrow> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mrow> <mo>=</mo> <mi>y</mi> <mrow> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for some <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2785_Article_IEq5.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="129" /> </InlineMediaObject> <EquationSource Format="TEX">$ {\hat{i}} \in \{1, 2, \cdots , m\}$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mover accent="true"> <mi>i</mi> <mo stretchy="false">^</mo> </mover> <mo>∈</mo> <mrow> <mo stretchy="false">{</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <mi>m</mi> <mo stretchy="false">}</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2785_Article_IEq6.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">$\theta > 0$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>θ</mi> <mo>></mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

Pursuit Differential Game Problem with Component-wise Constraints in $l_\infty $

期刊论文
发表日期：

2025年7月28日

查看全文

Bara’atu Bashir Borodo,
Ma’aruf Shehu Minjibir,
Abbas Ja’afaru Badakaya

摘要

A pursuit differential game problem with players’ motions and controls in the sequence space $l_\infty $ $l_{\infty}$ is considered in this paper. Controls of finite number of pursuers and one evader are subject to component-wise integral constraints. It has been established that there exist admissible strategies of pursuers such that $x_{{\hat{i}}}(\theta ) = y(\theta )$ $x_{\hat{i}} (θ) = y (θ)$ for some $ {\hat{i}} \in \{1, 2, \cdots , m\}$ $\hat{i} \in {1, 2, \dots, m}$ and $\theta > 0$ $θ > 0$ .

Pursuit Differential Game Problem with Component-wise Constraints in \(l_\infty \)

摘要