Computational aspects of reduced basis feedback controllers for spatially distributed systems

Two variations of a method for reducing controllers for systems described by partial differential equations (PDEs) are compared. In the first method, the controller reduction is accomplished by projection of a large scale finite element approximation of the PDE controller onto a low order basis that is computed using the proper orthogonal decomposition (POD). The second method involves computing a reduced order controller using the low order POD basis. An advantage to the first method is that the low order compensator retains more of the information of the full order controller since it is obtained through a projection. An advantage to the second method is that it is computationally more tractable as it does not require the full order compensator matrices. Simulations are included.