Late-lumping backstepping control of partial differential equations

Jean Auriol (1) , Kirsten A. Morris (2) , Florent Di Meglio (1)

1 CAS - Centre Automatique et Systèmes
2 University of Waterloo [Waterloo]

We consider in this paper three different partial differential equations (PDEs) that can be exponentially stabilized using backstepping controllers. For implementation, a finite-dimensional controller is generally needed. The backstepping controllers are approximated and it is proven that the finite-dimensional approximated controller stabilizes the original system if the order is high enough. This approach is known as late-lumping. The other approach to controller design for PDE’s first approximates the PDE and then a controller is designed; this is known as early lumping. Simulation results comparing the performance of late-lumping and early-lumping controllers are provided.

Mots clés: partial differential equations; backstepping; stabilization; late-lumping

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

Jean Auriol, Kirsten A. Morris, Florent Di Meglio. Late-lumping backstepping control of partial differential equations. Automatica, 2019, 100, pp.247 - 259. ⟨10.1016/j.automatica.2018.11.024⟩. ⟨hal-01740646⟩