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Delay-robust stabilization of a hyperbolic PDE–ODE system

Authors: Jean Auriol, Federico Bribiesca Argomedo, David Bou Saba, Michaël Di Loreto, Florent Di Meglio, Automatica, Elsevier, 2018, 95, pp.494 - 502, 2018, DOI: 10.1016/j.automatica.2018.06.033
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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.
author = {Federico Bribiesca Argomedo Jean Auriol, David Bou Saba, Michaël Di Loreto, Florent Di Meglio},
title = {Delay-robust stabilization of a hyperbolic PDE–ODE system},
journal = {Automatica},
volume = {95},
number = {},
pages = {494 - 502.},
year = {2018},