In this paper we consider an integrodifferential system, which governs the vibration of a viscoelastic one-dimensional object. We assume that we can act on the system at the boundary and we prove that it is possible to control both the position and the velocity at every point of the body and at a certain time T, large enough. We shall prove this result using moment theory and we shall prove that the solution of this problem leads to identification of a Riesz sequence which solves controllability and observability. The results presented here are constructive and can lead to simple numerical algorithms.
BOUNDARY CONTROLLABILITY AND OBSERVABILITY OF A VISCOELASTIC STRING / Loreti, Paola; L., Pandolfi; Sforza, Daniela. - In: SIAM JOURNAL ON CONTROL AND OPTIMIZATION. - ISSN 0363-0129. - STAMPA. - 50:2(2012), pp. 820-844. [10.1137/110827740]
BOUNDARY CONTROLLABILITY AND OBSERVABILITY OF A VISCOELASTIC STRING
LORETI, Paola;SFORZA, Daniela
2012
Abstract
In this paper we consider an integrodifferential system, which governs the vibration of a viscoelastic one-dimensional object. We assume that we can act on the system at the boundary and we prove that it is possible to control both the position and the velocity at every point of the body and at a certain time T, large enough. We shall prove this result using moment theory and we shall prove that the solution of this problem leads to identification of a Riesz sequence which solves controllability and observability. The results presented here are constructive and can lead to simple numerical algorithms.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
