Single input controllability of a simplified fluid-structure interaction model

Yuning Liu (1) , Takéo Takahashi (2, 3) , Marius Tucsnak (2, 3)

1 UR - Universität Regensburg
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECL - Institut Élie Cartan de Lorraine

In this paper we study a controllability problem for a simpli ed one dimensional model for the motion of a rigid body in a viscous uid. The control variable is the velocity of the uid at one end. One of the novelties brought in with respect to the existing literature consists in the fact that we use a single scalar control. Moreover, we introduce a new methodology, which can be used for other nonlinear parabolic systems, independently of the techniques previously used for the linearized problem. This methodology is based on an abstract argument for the null controllability of parabolic equations in the presence of source terms and it avoids tackling linearized problems with time dependent coefficients.

Mots clés: viscous Burgers equation; Null-controllability; fluid-structure interaction

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]

Yuning Liu, Takéo Takahashi, Marius Tucsnak. Single input controllability of a simplified fluid-structure interaction model. ESAIM: Control, Optimisation and Calculus of Variations, 2013, 19 (1), pp.20-42. ⟨10.1051/cocv/2011196⟩. ⟨hal-00922193⟩