Approximation of the controls for the linear beam equation

作者：Micu Sorin^*; Roventa Ionel; Temereanca Laurentiu Emanuel

来源：Mathematics of Control Signals and Systems, 2016, 28(2): 12.

DOI：10.1007/s00498-016-0161-x

• Beam equation
• Boundary control approximation
• HUM controls
• Filtering
• Regularity
• Moment problem
• Biorthogonals

This article deals with the approximation of the boundary controls of a 1-D linear equation modeling the transversal vibrations of a hinged beam using a finite-difference space semi-discrete scheme. Due to the high frequency numerical spurious oscillations, the semi-discrete model is not uniformly controllable with respect to the mesh size and the convergence of the approximate controls corresponding to initial data in the finite energy space cannot be guaranteed. In this paper we analyze how do the initial data to be controlled and their discretization affect the result of the approximation process. We prove that the convergence of the scheme is ensured if the continuous initial data are sufficiently regular or if the highest frequencies of their discretization have been filtered out. In both cases, the minimal weighted L-2-norm discrete controls are shown to be convergent to the corresponding continuous one when the mesh size tends to zero.

• 出版日期2016-6