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Delay robust control design of under-actuated PDE-ODE-PDE systems

Abstract : We propose a controller design for a system composed of two sets of linear heterodirectional hyperbolic PDEs, with actuation at one boundary, and coupled at the other boundary by ODEs in a PDE-ODE-PDE configuration. The design approach employs a backstepping transformation, however, the under-actuation limits the choice of target system. To deal with this limitation, we propose to use stability results from delay systems to find a stable target system. Furthermore, we propose to use a high-pass filter of the proximal reflection, in place of cancellation, to obtain controllers that are robust to small delays.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-02437344
Contributor : François Chaplais <>
Submitted on : Monday, January 13, 2020 - 5:13:25 PM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM

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Ulf Jakob F. Aarsnes, Rafael Vazquez, Florent Di Meglio, Miroslav Krstic. Delay robust control design of under-actuated PDE-ODE-PDE systems. 2019 American Control Conference (ACC), Jul 2019, Philadelphia, United States. pp.3200-3205, ⟨10.23919/ACC.2019.8814788⟩. ⟨hal-02437344⟩

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