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Robust control design of underactuated 2 × 2 PDE-ODE-PDE systems

Abstract : In this paper, we design a robust stabilizing controller for a system composed of two sets of linear heterodirec-tional hyperbolic PDEs, with actuation at one boundary of one of the PDEs, and couplings at the middle boundary with ODEs in a PDE-ODE-PDE configuration. The system is underactuated since only one of the PDE systems is actuated. The design approach employs a backstepping transformation to move the undesired system couplings to the proximal boundary (where the actuation is located). We can then express this target system as a time-delay neutral system for which we can design an appropriate control law to obtain an exponentially stable target system.
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https://hal.archives-ouvertes.fr/hal-02931065
Contributor : Jean Auriol <>
Submitted on : Friday, September 4, 2020 - 5:55:47 PM
Last modification on : Wednesday, April 14, 2021 - 3:41:05 AM
Long-term archiving on: : Wednesday, December 2, 2020 - 8:53:45 PM

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Jean Auriol, Jakob Ulf, Florent Di Meglio, Roman Shor. Robust control design of underactuated 2 × 2 PDE-ODE-PDE systems. IEEE Control Systems Letters, IEEE, 2021, 5 (2), pp.469-474. ⟨10.1109/lcsys.2020.3003514⟩. ⟨hal-02931065⟩

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