Delay-robust stabilization of a hyperbolic PDE–ODE system

• Autores: Jean-Claude Auriol, Federico Bribiesca Argomedo, David Bou Saba, Michaël Di Loreto, Florent Di Meglio
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 95, 2018, págs. 494-502
• Idioma: inglés
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• Resumen

  • We detail in this article the development of a delay-robust stabilizing feedback control law for a linear ordinary differential equation coupled with two linear first order hyperbolic equations in the actuation path. The proposed method combines the use of a backstepping approach, required to construct a canceling feedback for the in-domain coupling terms of the PDEs, with a second change of variables that reduces the stabilization problem of the PDE–ODE system to that of a time-delay system for which a predictor can be constructed. The proposed controller can be tuned, with some restrictions imposed by the system structure, either by adjusting a reflection coefficient left on the PDE after the backstepping transformation, or by choosing the pole placement on the ODE when constructing the predictor, enabling a trade-off between convergence rate and delay-robustness. The proposed feedback law is finally proved to be robust to small delays in the actuation.