Null controllability of the structurally damped wave equation with moving point control

Philippe Martin (1) , Lionel Rosier (2, 3) , Pierre Rouchon (1)

1 CAS - Centre Automatique et Systèmes
2 CORIDA - Robust control of infinite dimensional systems and applications
3 IECL - Institut Élie Cartan de Lorraine

We investigate the internal controllability of the wave equation with structural damping on the one-dimensional torus. We assume that the control is acting on a moving point or on a moving small interval with a constant velocity. We prove that the null controllability holds in some suitable Sobolev space and after a fixed positive time independent of the initial conditions.

Mots clés: Benjamin--Bona--Mahony equation; moment problem; moving control; multiplier; biorthogonal sequence; Korteweg--de Vries equation; structurally damped wave equation; null controllability; sine-type function

Domaines: Sciences de l'ingénieur [physics]; Automatique / Robotique

Philippe Martin, Lionel Rosier, Pierre Rouchon. Null controllability of the structurally damped wave equation with moving point control. SIAM Journal on Control and Optimization, 2013, 51 (1), pp.660-684. ⟨10.1137/110856150⟩. ⟨hal-00829857⟩