Small-time global stabilization of the viscous Burgers equation with three scalar controls

Jean-Michel Coron (1, 2, 3) , Shengquan Xiang (1, 2, 3)

1 SU - Sorbonne Université
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 CaGE - Control And GEometry

We construct explicit time-varying feedback laws leading to the global (null) stabilization in small time of the viscous Burgers equation with three scalar controls. Our feedback laws use first the quadratic transport term to achieve the small-time global approximate stabilization and then the linear viscous term to get the small-time local stabilization.

Mots clés: Time-varying feedback laws; Burgers equations; Small-time global stabilization; Backstepping; Controllability

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Jean-Michel Coron, Shengquan Xiang. Small-time global stabilization of the viscous Burgers equation with three scalar controls. Journal de Mathématiques Pures et Appliquées, 2021, 151 (9), pp.212-256. ⟨10.1016/j.matpur.2021.03.001⟩. ⟨hal-01723188⟩