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

Authors: Jean Auriol, Ulf Aarsnes, Philippe Martin, Florent Di Meglio, IEEE trans. Automatic Control, Vol. 63, No. 10, pp. 3551 - 3557, October 2018, DOI: 10.1109/TAC.2018.2798818

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.

BibTeX:

@Article{,

author = {Jean Auriol, Ulf Aarsnes, Philippe Martin, Florent Di Meglio},

title = {Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs},

journal = {IEEE trans. Automatic Control},

volume = {63},

number = {10},

pages = {3551 – 3557},

year = {2018},

abstract = {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.}, }

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.

BibTeX:

@Article{,

author = {Jean Auriol, Ulf Aarsnes, Philippe Martin, Florent Di Meglio},

title = {Delay-Robust Control Design for Two Heterodirectional Linear Coupled Hyperbolic PDEs},

journal = {IEEE trans. Automatic Control},

volume = {63},

number = {10},

pages = {3551 – 3557},

year = {2018},

abstract = {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.}, }