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<p>This paper investigates distributed <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(H_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> time-varying formation tracking of three-degree-of-freedom (3-DOF) unmanned surface vehicles within a singular control framework under jointly connected switching topologies. To tackle the associated control challenges, a distributed integral sliding-mode protocol is constructed together with a nonlinear disturbance observer(NDO), which is designed to handle time-varying external perturbations whose residual is <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(L_2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>L</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation>-integrable. Then, an energy-based <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(H_\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> criterion is imposed to restrict the closed-loop gain from residual disturbances to formation-tracking errors. Furthermore, by employing Laplacian decomposition under joint connectivity and a Cauchy-type convergence argument, sufficient linear matrix inequality (LMI) conditions are established to ensure admissibility as well as the feasibility of the prescribed time-varying formation tracking task. The resulting distributed gains are explicitly computable and only require local relative-state information. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed singular control approach.</p>

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Distributed \(H_{\infty }\) Time-Varying Formation Tracking of 3-DOF USVs: A Singular Control Approach

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Shaoyan Liu,
  • Hua Chen,
  • Mengqiu Shen,
  • Yun Chen

摘要

This paper investigates distributed \(H_\infty \) H ∞ time-varying formation tracking of three-degree-of-freedom (3-DOF) unmanned surface vehicles within a singular control framework under jointly connected switching topologies. To tackle the associated control challenges, a distributed integral sliding-mode protocol is constructed together with a nonlinear disturbance observer(NDO), which is designed to handle time-varying external perturbations whose residual is \(L_2\) L 2 -integrable. Then, an energy-based \(H_\infty \) H ∞ criterion is imposed to restrict the closed-loop gain from residual disturbances to formation-tracking errors. Furthermore, by employing Laplacian decomposition under joint connectivity and a Cauchy-type convergence argument, sufficient linear matrix inequality (LMI) conditions are established to ensure admissibility as well as the feasibility of the prescribed time-varying formation tracking task. The resulting distributed gains are explicitly computable and only require local relative-state information. Finally, numerical simulations are provided to demonstrate the effectiveness of the proposed singular control approach.