Optimization on a Grassmann manifold with application to system identification

In this paper, we consider the problem of optimization of a cost function on a Grassmann manifold. This problem appears in system identification in the behavioral setting, which is a structured low-rank approximation problem. We develop an optimization approach based on switching coordinate charts. This method reduces the optimization problem on the manifold to an optimization problem in a bounded domain of a Euclidean space. We compare the proposed approach with state-of-the-art methods based on data-driven local coordinates and Riemannian geometry, and show the connections between the methods. Compared to the methods based on the local coordinates, the proposed approach allows to use arbitrary optimization methods for solving the corresponding subproblems in the Euclidean space.