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Switching event-triggered control of nonlinear parabolic PDE systems via Galerkin/neural-network-based modeling approach

Author

Listed:
  • Sun, Xiaoyu
  • Zhang, Chuan
  • Wu, Huai-Ning
  • Zhang, Xianfu

Abstract

This study proposes an innovative switching ET (event-triggered) control framework for parabolic partial differential equation (PDE) systems under dual uncertainties from unknown dynamics and external disturbances. First, a dual-scale decomposition integrating multilayer neural networks and Galerkin spectral methods to decouple PDE dynamics into relatively accurate slow/fast subsystems and enable model-free nonlinearity identification via Levenberg-Marquardt algorithm. Second, a dwell-time-regulated switching ET mechanism significantly reducing communication frequency compared to conventional periodic sampling or static ET while guaranteeing to avoid Zeno behavior through time-domain constraints. Third, sub-optimal H∞ performance is achieved via an iterative algorithm based on the alternating optimization of convex linear matrix inequality subproblems. Finally, validated through two numerical simulations: catalytic reactor and traffic flow, the framework establishes a new paradigm for industrial thermal-chemical processes requiring reliability under communication constraints.

Suggested Citation

  • Sun, Xiaoyu & Zhang, Chuan & Wu, Huai-Ning & Zhang, Xianfu, 2026. "Switching event-triggered control of nonlinear parabolic PDE systems via Galerkin/neural-network-based modeling approach," Applied Mathematics and Computation, Elsevier, vol. 515(C).
    • Handle: RePEc:eee:apmaco:v:515:y:2026:i:c:s0096300325005582
    DOI: 10.1016/j.amc.2025.129833
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    References listed on IDEAS

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    1. Xi-Ming Liu & Xiao-Heng Chang & Li-Wei Hou, 2024. "Attack-Dependent Adaptive Event-Triggered Security Fuzzy Control for Nonlinear Networked Cascade Control Systems Under Deception Attacks," Mathematics, MDPI, vol. 12(21), pages 1-24, October.
    2. Elayabharath, V.T. & Sozhaeswari, P. & Tatar, N. & Sakthivel, R. & Satheesh, T., 2025. "Resilient observer-based unified state and fault estimation for nonlinear parabolic PDE systems via fuzzy approach over finite-time interval," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    3. F. Lenz & D. Herde & A. Riegert & H. Kantz, 2009. "Bivariate time-periodic Fokker-Planck model for freeway traffic," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(3), pages 467-472, December.
    4. Li, Xing-Yu & Wu, Kai-Ning & Yang, Zhan-Wen, 2025. "Exponential stabilization for spatial multiple-fractional advection-diffusion-reaction system," Applied Mathematics and Computation, Elsevier, vol. 499(C).
    Full references (including those not matched with items on IDEAS)

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