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<p>In this paper, a novel robust control method with prescribed performance is proposed for a class of strict-feedback parameter-varying systems with external disturbances. First, a finite-time performance function is designed to limit the tracking error of the system and to make the system satisfy the steady-state and transient performance constraints. Notably, compared with traditional prescribed performance control, the performance function designed in this paper can make the tracking error converge in finite time. Subsequently, the effects of external disturbances on the system are attenuated by <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11071_2025_11167_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="29" /> </InlineMediaObject> <EquationSource Format="TEX">\({H_\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> control. The backstepping method is used to design the controller, and dynamic surface control is introduced to solve the differential explosion problem in the backstepping procedure. Finally, simulation examples on a numerical strict-feedback parameter-varying system and a rigid robot manipulator system are provided to show the effectiveness of the proposed method. The control strategy proposed in this paper effectively rejects external disturbances while ensuring that the closed-loop system satisfies preset constraints on steady-state error, settling time, and overshoot.</p>

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\(H_{\infty }\) control of strict-feedback parameter-varying systems with multiple performance constraints

  • 期刊论文

  • 发表日期：

    2025年4月18日

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  • Jiaxi Zhang,
  • Jianping Zeng,
  • Hongfei Sun

摘要

In this paper, a novel robust control method with prescribed performance is proposed for a class of strict-feedback parameter-varying systems with external disturbances. First, a finite-time performance function is designed to limit the tracking error of the system and to make the system satisfy the steady-state and transient performance constraints. Notably, compared with traditional prescribed performance control, the performance function designed in this paper can make the tracking error converge in finite time. Subsequently, the effects of external disturbances on the system are attenuated by \({H_\infty }\) H ∞ control. The backstepping method is used to design the controller, and dynamic surface control is introduced to solve the differential explosion problem in the backstepping procedure. Finally, simulation examples on a numerical strict-feedback parameter-varying system and a rigid robot manipulator system are provided to show the effectiveness of the proposed method. The control strategy proposed in this paper effectively rejects external disturbances while ensuring that the closed-loop system satisfies preset constraints on steady-state error, settling time, and overshoot.