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<p>The adaptive <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11768_2025_262_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{H}_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>H</mtext> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system (NSHS) in this article. Under an appropriate adaptive state feedback, the NSHS can be equivalently transformed into a differential-algebraic system. Next, it is proved that the state feedback can be used as an adaptive <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11768_2025_262_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{H}_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>H</mtext> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> finite-time boundedness controller of NSHS. Finally, the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.</p>

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Adaptive \(\textrm{H}_\infty \) finite-time boundedness control for a set of nonlinear singular Hamiltonian systems

  • 期刊论文

  • 发表日期：

    2025年7月9日

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  • Shuhua He,
  • Liying Sun,
  • Renming Yang

摘要

The adaptive \(\textrm{H}_\infty \) H ∞ finite-time boundedness control problem is studied for a set of nonlinear singular Hamiltonian system (NSHS) in this article. Under an appropriate adaptive state feedback, the NSHS can be equivalently transformed into a differential-algebraic system. Next, it is proved that the state feedback can be used as an adaptive \(\textrm{H}_\infty \) H ∞ finite-time boundedness controller of NSHS. Finally, the effectiveness of the controller designed is verified by an illustrative example of a nonlinear singular circuit system.