Boundary feedback control of an anti-stable wave equation

Pierre Apkarian (1) , Dominikus Noll (2)

1 DTIS, ONERA, Université de Toulouse [Toulouse]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We discuss boundary control of a wave equation with a non-linear antidamping boundary condition. We design structured finite-dimensional H ∞-output feedback controllers which stabilize the infinite dimensional system exponentially in closed loop. The method is applied to control torsional vibrations in drilling systems with the goal to avoid slip-stick.

Mots clés: Wave equation; Boundary feedback control; Anti-damping boundary; Infinite-dimensional H∞-control; Slip-stick; Torsional vibrations; Large magnitude sector non-linearity

Domaines: Sciences de l'ingénieur [physics]; Physique [physics]; Informatique [cs]

Pierre Apkarian, Dominikus Noll. Boundary feedback control of an anti-stable wave equation. IMA Journal of Mathematical Control and Information, 2020, 37 (4), pp.1367-1399. ⟨10.1093/imamci/dnaa017⟩. ⟨hal-03188075⟩