An approximation scheme for the LQG control of flexible structures

This paper deals with the LQG control problem of flexible structures. Since the solution to this problem is given by infinite dimension equations, an approximation scheme is necessary to find an implementable control law. Here a Galerkin approach is used. The novelty of the paper is the successful use of the eigenfunctions of the system instead of usual splines to build up finite dimensional approximating subspaces. By using the Trotter-Kato theorem, it is proved that the state of the system evolving when the approximating input is applied converges in L₂ norm to the state evolving when the optimal one is applied.