Stabilization of a hyperbolic PDEs-ODE network using a recursive dynamics interconnection framework

Jean Auriol (1) , Federico Bribiesca Argomedo (2) , Silviu-Iulian Niculescu (1) , Jeanne Redaud (1, 3)

1 L2S - Laboratoire des signaux et systèmes
2 AIS - Ampère, Département Automatique pour l'Ingénierie des Systèmes
3 DISCO - Dynamical Interconnected Systems in COmplex Environments

In this paper, we design a state-feedback law that exponentially stabilizes an underactuated network of scalar hyperbolic systems coupled at the end of the chain with a finite-dimensional system modeled by an ordinary differential equation. Our approach uses a recursive dynamics interconnection framework. More precisely, for each subsystem, we solve a stabilization problem, a tracking problem and design a statepredictor. Then, we are able to recursively design a control law that stabilizes the whole chain. Some illustrative examples complete the presentation.

Domaines: Mathématiques [math]; Sciences de l'ingénieur [physics]

Jean Auriol, Federico Bribiesca Argomedo, Silviu-Iulian Niculescu, Jeanne Redaud. Stabilization of a hyperbolic PDEs-ODE network using a recursive dynamics interconnection framework. ECC 2021 - European Control Conference, Jun 2021, Rotterdam (virtual), Netherlands. ⟨10.23919/ecc54610.2021.9654865⟩. ⟨hal-03185012⟩