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Delay-robust control design for two heterodirectional linear coupled hyperbolic PDEs

Abstract : We detail in this article the necessity of a change of paradigm for the delay-robust control of systems composed of two linear first order hyperbolic equations. One must go back to the classical trade-off between convergence rate and delay-robustness. More precisely, we prove that, for systems with strong reflections, canceling the reflection at the actuated boundary will yield zero delay-robustness. Indeed, for such systems, using a backstepping-controller, the corresponding target system should preserve a small amount of this reflection to ensure robustness to a small delay in the loop. This implies, in some cases, giving up finite time convergence.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-01585911
Contributor : Jean Auriol <>
Submitted on : Tuesday, September 12, 2017 - 10:48:25 AM
Last modification on : Thursday, September 24, 2020 - 5:04:18 PM
Long-term archiving on: : Wednesday, December 13, 2017 - 5:16:54 PM

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  • HAL Id : hal-01585911, version 1
  • ARXIV : 1709.04274

Citation

Jean Auriol, Ulf Aarsnes, Philippe Martin, Florent Meglio. Delay-robust control design for two heterodirectional linear coupled hyperbolic PDEs. IEEE Transactions on Automatic Control, Institute of Electrical and Electronics Engineers, 2018. ⟨hal-01585911⟩

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