An Approximation Method for Exact Controls of Vibrating Systems

Abstract

We propose a new method for the approximation of exact controls of a second order infinite dimensional system with bounded input operator. The algorithm combines Russell's “stabilizability implies controllability” principle with the Galerkin method. The main new feature of this work consists of giving precise error estimates. In order to test the efficiency of the method, we consider two illustrative examples (with the finite element approximations of the wave and the beam equations) and describe the corresponding simulations.