Skip to content
DraconiticResearch
Search Sources API
197,768 studies31 sourcesUpdated 5 min ago
PreprintCC BY 4.0HAL

Observing hyperbolic systems with source and dynamic boundary disturbances

  • Jiahao Wu
  • Emmanuelle Crépeau
  • Christophe Prieur
  • Liguo Zhang
Open at sourcePDFCite

Abstract

This paper investigates the problem of adaptive boundary observers design for a class of coupled linear ODEhyperbolic PDE systems. The system is subject to source and dynamic boundary disturbances, namely two distinct parametric uncertainties, which affect both the PDE domain equations and the coupled ODE equations. Utilizing two swapping transformations, we introduce Luenberger-type boundary observers with a parameter adaptive law. These observers efficiently estimate the ODE-PDE states and unknown parameters simultaneously, relying solely on measurements at the boundaries of the PDE side. By employing the Lyapunov technique, we derive sufficient conditions in terms of matrix inequalities for the constant observer gain to ensure the exponential convergence of the estimation errors with respect to suitable norms. Finally, we illustrate the effectiveness of the adaptive boundary observer scheme through a numerical example.

Related

  1. Minimal control time of some 1D first-order linear hyperbolic systems with row rank deficient boundary coupling matrix
    Long Hu, Guillaume Olive, Zengzhi Xin
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  2. Boundary stabilization of multi-dimensional first-order quasilinear hyperbolic systems
    Haitian Yang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  3. Exponential Turnpike in Optimal Boundary Control of Multi-Dimensional First-Order Hyperbolic Systems
    Haitian Yang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsOptimisation & controlarXiv
  4. Input-to-state stability of second-order port-Hamiltonian systems under nonlinear dynamic boundary feedback
    Bouchra Elghazi, Birgit Jacob, Christophe Prieur
    arXivPreprintCC BY 4.0Full textOptimisation & controlarXiv
  5. Robust Iterative Learning Control for Multi-Agent Systems with Random Impulsive Disturbances
    Zijian Luo, Hongyu Yang, Qianqian Zhang
    AxiomsPeer-reviewedCC BY 4.0General mathematicsCrossref

Cite

BibTeXRIS
BibTeX
@misc{wu2026observing,
  title = {{Observing hyperbolic systems with source and dynamic boundary disturbances}},
  author = {Jiahao Wu and Emmanuelle Crépeau and Christophe Prieur and Liguo Zhang},
  howpublished = {HAL},
  year = {2026},
  month = nov,
  url = {https://hal.science/hal-05852978v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Observing hyperbolic systems with source and dynamic boundary disturbances
AU  - Jiahao Wu
AU  - Emmanuelle Crépeau
AU  - Christophe Prieur
AU  - Liguo Zhang
PY  - 2026
DA  - 2026/11/05
PB  - HAL
UR  - https://hal.science/hal-05852978v1
AB  - This paper investigates the problem of adaptive boundary observers design for a class of coupled linear ODEhyperbolic PDE systems. The system is subject to source and dynamic boundary disturbances, namely two distinct parametric uncertainties, which affect both the PDE domain equations and the coupled ODE equations. Utilizing two swapping transformations, we introduce Luenberger-type boundary observers with a parameter adaptive law. These observers efficiently estimate the ODE-PDE states and unknown parameters simultaneously, relying solely on measurements at the boundaries of the PDE side. By employing the Lyapunov technique, we derive sufficient conditions in terms of matrix inequalities for the constant observer gain to ensure the exponential convergence of the estimation errors with respect to suitable norms. Finally, we illustrate the effectiveness of the adaptive boundary observer scheme through a numerical example.
ER  -