Delay-robust control design for heterodirectional linear coupled hyperbolic PDEs

Jean Auriol, Ulf Jakob Fl Aarsnes, Philippe Martin, Florent Di Meglio
2018 IEEE Transactions on Automatic Control  
Norway and DrillWell -Drilling and well centre for improved recovery Stavanger, Norway 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 delayrobustness. Indeed,
more » ... bustness. 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.
doi:10.1109/tac.2018.2798818 fatcat:jqrxwvcq6vfrrekqtgdgoyv6ky