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

Philippe Martin 1 Lionel Rosier 2, 3 Pierre Rouchon 1
2 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
Abstract : 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.
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Philippe Martin, Lionel Rosier, Pierre Rouchon. Null controllability of the structurally damped wave equation with moving point control. SIAM Journal on Control and Optimization, Society for Industrial and Applied Mathematics, 2013, 51 (1), pp.660-684. ⟨10.1137/110856150⟩. ⟨hal-00829857⟩

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