Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs

We detail in this paper the importance of a change of strategy for the delay robust control of systems composed of two linear first-order hyperbolic equations. One must go back to the classical tradeoff between convergence rate and delay robustness. More precisely, we prove that, for systems with st...

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Bibliographic Details
Published inIEEE transactions on automatic control Vol. 63; no. 10; pp. 3551 - 3557
Main Authors Auriol, Jean, Aarsnes, Ulf Jakob Flo, Martin, Philippe, Meglio, Florent Di
Format Journal Article
LanguageEnglish
Published New York IEEE 01.10.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Institute of Electrical and Electronics Engineers
Subjects
Analysis of PDEs
Automatic
Backstepping
Convergence
Couplings
Delay
delay robustness
Delays
Engineering Sciences
hyperbolic partial differential equations (PDEs)
Mathematical model
Mathematics
Reflection
Robust control
Robustness
stabilization
Transfer functions
backstepping
Hyperbolic Partial Differential Equations
stabilization
delay-robustness
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Summary:We detail in this paper the importance of a change of strategy for the delay robust control of systems composed of two linear first-order hyperbolic equations. One must go back to the classical tradeoff 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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2018.2798818