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

Jean F Auriol (1) , Ulf J.F Aarsnes (2) , Philippe Martin (1) , Florent Di Meglio (1)

1 CAS - Centre Automatique et Systèmes
2 IRIS - International Research Institute of Stavanger

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.

Mots clés: Hyperbolic Partial Differential Equations; stabilization; backstepping; delay-robustness

Domaines: Equations aux dérivées partielles [math.AP]; Automatique / Robotique

Jean F Auriol, Ulf J.F Aarsnes, Philippe Martin, Florent Di Meglio. Delay-robust control design for two heterodirectional linear coupled hyperbolic PDEs. IEEE Transactions on Automatic Control, 2018. ⟨hal-01585911⟩