An approximation technique for computing optimal fixed-order controllers for infinite-dimensional systems

The authors consider the finite-dimensional approximation of the infinite-dimensional optimal projection theory of Bernstein and Hyland (1984, 1986), the purpose being model and controller order reduction. The approach yields fixed-finite-order controllers which are optimal with respect to high-order, approximating, finite-dimensional plant models. The authors illustrate the technique by computing a sequence of first-order controllers, for a one-dimensional, single-input/single-output, parabolic (heat/diffusion) system using a spline-based, Ritz-Galerkin, finite-element approximation. The numerical studies indicate convergence of the feedback gains with less than 2% performance degradation over full-order LQG controllers