Adaptive Synchronization for Networked Parabolic PDE Systems with Uncertain Nonlinear Actuator Dynamics

Yukan Zheng, Yuan Xin Li, Choon Ki Ahn

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


This article focuses on the synchronization control of networked uncertain parabolic partial differential equations (PDEs) with uncertain nonlinear actuator dynamics. Compared to existing networked PDE systems, control input occurs in ordinary differential equation (ODE) subsystems rather than in PDE ones. Compared to existing results, where the exact system parameters must be known for the entire system, this paper further considers parabolic PDE-ODE systems with unknown parameters affecting the interior of the PDE domain. Due to the unknown parameters and uncertain nonlinear actuator dynamics, the existing distributed algorithms and stability analysis tools cannot be utilized to solve the synchronization problem of cascaded parabolic systems. To address this difficulty, this study designs a novel passive identifier to estimate the states and unknown parameters. Subsequently, based on the passive identifier and Lyapunov function method, a synchronization controller is presented for cascaded parabolic PDE systems to ensure that the synchronization control and the boundedness of all the closed-loop signals are achieved. Lastly, the effectiveness of the obtained results is illustrated using simulation.

Original languageEnglish
Pages (from-to)2167-2178
Number of pages12
JournalIEEE Transactions on Circuits and Systems I: Regular Papers
Issue number5
Publication statusPublished - 2023 May 1

Bibliographical note

Publisher Copyright:
© 2004-2012 IEEE.


  • Synchronization
  • actuator dynamics
  • multi-agent systems
  • nonlinearity
  • parabolic PDE
  • uncertainty

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Hardware and Architecture


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