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<p>This paper focuses on the design of a fuzzy state observer for spatial two-dimensional (2-D) nonlinear parabolic partial differential equation (PDE) systems using mobile sensors. Aiming at the actual physical process, the spatial 2-D case makes more sense. With the increase of space dimension, the difficulty of system design increases significantly. First of all, a Takagi-Sugeno (T-S) fuzzy model is utilized to accurately represent the 2-D nonlinear PDE systems. Subsequently, the 2-D spatial domain is partitioned into multiple subdomains on the grounds of the quantity of sensors, and a projection design idea is employed to ensure that the mobile sensors move within a prescribed area. Then, using the Poincar<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\acute{e}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mi>e</mi> <mo>´</mo> </mover> </math></EquationSource> </InlineEquation>-Wirtinger inequality and Barbalat lemma, a Lyapunov-based design scheme is proposed to obtain the fuzzy state observer and the mobile sensor guidance laws, which is capable of making the state estimation error system asymptotically stable. Finally, numerical simulation is provided to illustrate the validity of the proposed approach.</p>

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Fuzzy state observer design for spatial 2-D nonlinear parabolic PDE systems under mobile sensors

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Xiao-Wei Zhang,
  • Xiao-Qiong Li,
  • Xiaoli Li,
  • Huai-Ning Wu,
  • Zi-Peng Wang

摘要

This paper focuses on the design of a fuzzy state observer for spatial two-dimensional (2-D) nonlinear parabolic partial differential equation (PDE) systems using mobile sensors. Aiming at the actual physical process, the spatial 2-D case makes more sense. With the increase of space dimension, the difficulty of system design increases significantly. First of all, a Takagi-Sugeno (T-S) fuzzy model is utilized to accurately represent the 2-D nonlinear PDE systems. Subsequently, the 2-D spatial domain is partitioned into multiple subdomains on the grounds of the quantity of sensors, and a projection design idea is employed to ensure that the mobile sensors move within a prescribed area. Then, using the Poincar \(\acute{e}\) e ´ -Wirtinger inequality and Barbalat lemma, a Lyapunov-based design scheme is proposed to obtain the fuzzy state observer and the mobile sensor guidance laws, which is capable of making the state estimation error system asymptotically stable. Finally, numerical simulation is provided to illustrate the validity of the proposed approach.