Model reduction for large-scale dynamical systems via equality constrained least squares

In this paper, we present a new method of model reduction for large-scale dynamical systems, which belongs to the SVD-Krylov based method category. It is a two-sided projection where one side reflects the Krylov part and the other side reflects the SVD (observability gramian) part. The reduced model matches the first r+i Markov parameters of the full order model, and the remaining ones approximate in a least squares sense without being explicitly computed, where r is the order of the reduced system, and i is a nonnegative integer such that 1≤i<r. The reduced system minimizes a weighted ?₂ error. By the definition of a shift operator, the proposed approximation is also obtained by solving an equality constrained least squares problem. Moreover, the method is generalized for moment matching at arbitrary interpolation points. Several numerical examples verify the effectiveness of the approach.